presentation of trigonometry for class 10

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Unit 15: Introduction to Trigonometry

Trigonometry 8.1.

• Intro to the trigonometric ratios (Opens a modal)
• Solving for a side in right triangles with trigonometry (Opens a modal)
• Finding reciprocal trig ratios (Opens a modal)
• Introduction to Trigonometry 8.1 10 questions Practice

Trigonometry 8.2

• Special right triangles intro (part 1) (Opens a modal)
• Special right triangles intro (part 2) (Opens a modal)
• 30-60-90 triangle example problem (Opens a modal)
• Introduction to Trigonometry 8.2 10 questions Practice

Trigonometry 8.3

• Intro to Pythagorean trigonometric identities (Opens a modal)
• Converting between trigonometric ratios example: write all ratios in terms of sine (Opens a modal)
• Trigonometric identity example proof involving sec, sin, and cos (Opens a modal)
• Trigonometric identity example proof involving sin, cos, and tan (Opens a modal)
• Trigonometric identity example proof involving all the six ratios (Opens a modal)
• Introduction to Trigonometry 8.3 6 questions Practice

Trigonometry

Aug 31, 2014

1.65k likes | 3.63k Views

Trigonometry. BY SAI KUMAR. Maths. Trigonometry. Trigonometry is derived from Greek words trigonon (three angles) and metron ( measure). Trigonometry is the branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees

Share Presentation

Trigonometry.

• computer music
• 1 cosq 1 cosq

Presentation Transcript

Trigonometry BY SAI KUMAR Maths

Trigonometry • Trigonometry is derived from Greek words trigonon (three angles) and metron ( measure). • Trigonometry is the branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees • Triangles on a sphere are also studied, in spherical trigonometry. • Trigonometry specifically deals with the relationships between the sides and the angles of triangles, that is, on the trigonometric functions, and with calculations based on these functions.

History • The origins of trigonometry can be traced to the civilizations of ancient Egypt, Mesopotamia and the Indus Valley, more than 4000 years ago. • Some experts believe that trigonometry was originally invented to calculate sundials, a traditional exercise in the oldest books • The first recorded use of trigonometry came from the Hellenistic mathematician Hipparchus circa 150 BC, who compiled a trigonometric table using the sine for solving triangles. • The Sulba Sutras written in India, between 800 BC and 500 BC, correctly compute the sine of π/4 (45°) as 1/√2 in a procedure for circling the square (the opposite of squaring the circle). • Many ancient mathematicians like Aryabhata, Brahmagupta,Ibn Yunus and Al-Kashi made significant contributions in this field(trigonometry).

Right Triangle • A triangle in which one angle is equal to 90 is called right triangle. • The side opposite to the right angle is known as hypotenuse. AB is the hypotenuse • The other two sides are known as legs. AC and BC are the legs Trigonometry deals with Right Triangles

Pythagoras Theorem • In any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of areas of the squares whose sides are the two legs. • In the figure AB2 = BC2 + AC2

Trigonometric ratios • Sine(sin) opposite side/hypotenuse • Cosine(cos) adjacent side/hypotenuse • Tangent(tan) opposite side/adjacent side • Cosecant(cosec) hypotenuse/opposite side • Secant(sec) hypotenuse/adjacent side • Cotangent(cot) adjacent side/opposite side

Values of trigonometric function of Angle A • sin = a/c • cos = b/c • tan = a/b • cosec = c/a • sec = c/b • cot = b/a

Values of Trigonometric function

Calculator • This Calculates the values of trigonometric functions of different angles. • First Enter whether you want to enter the angle in radians or in degrees. Radian gives a bit more accurate value than Degree. • Then Enter the required trigonometric function in the format given below: • Enter 1 for sin. • Enter 2 for cosine. • Enter 3 for tangent. • Enter 4 for cosecant. • Enter 5 for secant. • Enter 6 for cotangent. • Then enter the magnitude of angle.

Trigonometric identities • sin2A + cos2A = 1 • 1 + tan2A = sec2A • 1 + cot2A = cosec2A • sin(A+B) = sinAcosB + cosAsin B • cos(A+B) = cosAcosB – sinAsinB • tan(A+B) = (tanA+tanB)/(1 – tanAtan B) • sin(A-B) = sinAcosB – cosAsinB • cos(A-B)=cosAcosB+sinAsinB • tan(A-B)=(tanA-tanB)(1+tanAtanB) • sin2A =2sinAcosA • cos2A=cos2A - sin2A • tan2A=2tanA/(1-tan2A) • sin(A/2) = ±{(1-cosA)/2} • Cos(A/2)= ±{(1+cosA)/2} • Tan(A/2)= ±{(1-cosA)/(1+cosA)}

Relation between different Trigonometric Identities • Sin • Cos • Tan • Cosec • Sec • Cot

Angles of Elevation and Depression • Line of sight: The line from our eyes to the object, we are viewing. • Angle of Elevation:The angle through which our eyes move upwards to see an object above us. • Angle of depression:The angle through which our eyes move downwards to see an object below us.

Problem solved using trigonometric ratios CLICK HERE!

Applications of Trigonometry • This field of mathematics can be applied in astronomy, navigation, music theory, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound), pharmacy, chemistry, number theory (and hence cryptology), seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, economics, electrical engineering, mechanical engineering, civil engineering, computer graphics, cartography, crystallography and game development.

Derivations • Most Derivations heavily rely on Trigonometry. Click the hyperlinks to view the derivation • A few such derivations are given below:- Parallelogram law of addition of vectors . Centripetal Acceleration . Lens Formula . Variation of Acceleration due to gravity due to rotation of earth Finding angle between resultant and the vector.

Applications of Trigonometry in Astronomy • Since ancient times trigonometry was used in astronomy. • The technique of triangulation is used to measure the distance to nearby stars. • In 240 B.C., a mathematician named Eratosthenes discovered the radius of the Earth using trigonometry and geometry. • In 2001, a group of European astronomers did an experiment that started in 1997 about the distance of Venus from the Sun. Venus was about 105,000,000 kilometers away from the Sun .

Application of Trigonometry in Architecture • Many modern buildings have beautifully curved surfaces. • Making these curves out of steel, stone, concrete or glass is extremely difficult, if not impossible. • One way around to address this problem is to piece the surface together out of many flat panels, each sitting at an angle to the one next to it, so that all together they create what looks like a curved surface. • The more regular these shapes, the easier the building process. • Regular flat shapes like squares, pentagons and hexagons, can be made out of triangles, and so trigonometry plays an important role in architecture.

Waves • The graphs of the functions sin(x) and cos(x) look like waves. Sound travels in waves, although these are not necessarily as regular as those of the sine and cosine functions. • However, a few hundred years ago, mathematicians realized that any wave at all is made up of sine and cosine waves. This fact lies at the heart of computer music. • Since a computer cannot listen to music as we do, the only way to get music into a computer is to represent it mathematically by its constituent sound waves. • This is why sound engineers, those who research and develop the newest advances in computer music technology, and sometimes even composers have to understand the basic laws of trigonometry. • Waves move across the oceans, earthquakes produce shock waves and light can be thought of as traveling in waves. This is why trigonometry is also used in oceanography, seismology, optics and many other fields like meteorology and the physical sciences.

Digital Imaging • In theory, the computer needs an infinite amount of information to do this: it needs to know the precise location and colour of each of the infinitely many points on the image to be produced. In practice, this is of course impossible, a computer can only store a finite amount of information. • To make the image as detailed and accurate as possible, computer graphic designers resort to a technique called triangulation. • As in the architecture example given, they approximate the image by a large number of triangles, so the computer only needs to store a finite amount of data. • The edges of these triangles form what looks like a wire frame of the object in the image. Using this wire frame, it is also possible to make the object move realistically. • Digital imaging is also used extensively in medicine, for example in CAT and MRI scans. Again, triangulation is used to build accurate images from a finite amount of information. • It is also used to build "maps" of things like tumors, which help decide how x-rays should be fired at it in order to destroy it.

Conclusion Trigonometry is a branch of Mathematics with several important and useful applications. Hence it attracts more and more research with several theories published year after year

In each of the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios. • sinA = 2/3 • sinQ = 11/15 • cosQ = 7/25 • secQ=13/5 • cosA = 4/5 • Tan = 5/12 • tanQ =8/15

In a ABC, right angled at B, AB+24cm,BC=7 cm. Determine • sinA, cosA • sinC, cosC

(1+sinQ) (1-sinQ) If cotQ =7/8 ,evaluate (1=cosQ) (1-cosQ)

Evaluate each of the following • sin45 sin30 + cos45 cos30 • sin60 cos30 + cos60 sin30 • cos60 cos45 – sin60 sin45 • sin²30+sin²45+sin²60+sin²90 • cos²30+cos²45+cos²60+cos²90 • tan²30+tan²60+tan²45

Thanks to you 25

• More by User

Trigonometry. Angles of elevation and depression. Instructions for use. There are 5 worked examples shown in this PowerPoint plus explanations. A red dot will appear top right of screen to proceed to the next slide.

790 views • 11 slides

Trigonometry. Trigonometry begins in the right triangle, but it doesn’t have to be restricted to triangles. The trigonometric functions carry the ideas of triangle trigonometry into a broader world of real-valued functions and wave forms. . Trigonometry Topics. Radian Measure

1.49k views • 49 slides

1.31k views • 71 slides

TRIGONOMETRY

TRIGONOMETRY. An introduction.

2.46k views • 9 slides

Trigonometry. Calisia McLean. Trigonomic functions.

405 views • 11 slides

Find trigonometric ratios using right triangles. Solve problems using trigonometric ratios. trigonometry. trigonometric ratio sine cosine tangent.

516 views • 28 slides

Trigonometry. Right angled triangles. A triangle. Opposite and Adjacent are relative to the angle. The 4cm side is opposite to A The 6cm side is adjacent to A The 6cm side is opposite to B The 4cm side is adjacent to B. SOH CAH TOA Sine, Cosine & Tangent of an angle. SOH CAH TOA. SOH

870 views • 33 slides

Trigonometry. Pythagoras Theorem & Trigo Ratios of Acute Angles. Pythagoras Theorem. a 2 + b 2 = c 2. where c is the hypotenuse while a and b are the lengths of the other two sides. c. a. b. P. O. Q. Trigo Ratios of Acute angles. hypotenuse. opposite. adjacent.

1.02k views • 35 slides

Trigonometry. Describe what a bearing is. Describe what a bearing is. A bearing is a measurement of an angle from North in a clockwise direction. Do you know how to write a vector?. Do you know how to write a vector?. A vector is written like this. An example of a vector. 3. -4.

875 views • 55 slides

Trigonometry. 7.1b. 7.2. 7.3. 7.4. 7.1. 7.5. 100. 100. 100. 100. 100. 100. 200. 200. 200. 200. 200. 200. 300. 300. 300. 300. 300. 300. 400. 400. 400. 400. 400. 400. 500. 500. 500. 500. 500. 500. 600. 600. 600. 600. 600. 600. Credits. 7.1 - 100.

1.02k views • 73 slides

TRIGONOMETRY. CHAPTER 2. 2.2 Using the Tangent Ratio to Calculate Lengths. You knew the values of two legs and you calculated the value of an acute angle. Previously:. 2.2 Using the Tangent Ratio to Calculate Lengths.

319 views • 10 slides

Trigonometry. Fendy Lormine 6-5-13 F Block. A. Mimmy’s Pizza. B. 25. C. 7m. Mimmy has a slice of Pizza in the shape of a right triangle They tell her that angle C measures 25 degrees, line BC measures 7 meters. She’s asked to use Trigonometry to find AB.

241 views • 8 slides

Trigonometry. What is the acronym we use to remember trig functions?. SOH CAH TOA. Sin θ. Sin θ = 5/13. Tan θ=6/8=3/4. Write the ratio you would use to find x. Cos θ = x / 11. What ratio would you create given the information?. Cos θ = 4 / 5. Find x. Tan 32 = x / 13 X = 8.1°.

760 views • 52 slides

Trigonometry. By: Alicia , Eunice, Rochelle and Nisi. Learning the basics!. The  angle of elevation is the angle of looking up, measure from the horizontal. The angle of depression is the angle of looking down, measured from the horizontal. Statue Of Liberty. Background information!.

373 views • 8 slides

Trigonometry. Introduction By: Mushtaq ur Rehman. Instant Trig. Trigonometry is math, so many people find it scary It’s usually taught in a one-semester high-school course However, 95% of all the “trig” you’ll ever need to know can be covered in 15 minutes

408 views • 10 slides

Trigonometry. ACT Review. Definition of Trigonometry. It is a relationship between the angles and sides of a triangle. Radians. ( x,y ) = ( Rcos ( θ ) , Rsin ( θ ) ) ( 1 cos (30˚) , 1 sin (30 ˚) =. The radian is a unit of plane angle, equal to 180/π (or 360/(2π)) degrees

464 views • 22 slides

TRIGONOMETRY. Let’s have some fun!. With Tony the Triangle!!!. Click me!. Let’s Get Started!. Where to start…. Cosine. Sine. Tangent. Click here to begin. SOH-CAH-TOA. In Trigonometry the three basic functions that we will be learning about can be remembered by the pneumonic below:

979 views • 53 slides

T1.1 and T1.2. Trigonometry. To convert from degrees to radians multiply by Example: Convert 155 deg to radians Notice how the units cancel to leave radians!. Section T1.1 - Angle Conversion. To convert from radians to degrees multiply by Example: Convert radians to degrees

323 views • 14 slides

Trigonometry. Objectives: The Student Will … Find trigonometric ratios using right Triangles Solve problems using trigonometric ratios. HOMEWORK: Sin, cos, tan Practice WS `. Sine =. Cosine =. Tangent =. Trigonometric Ratios. SOH CAH TOA. Opposite. Hypotenuse. Adjacent.

381 views • 14 slides

TRIGONOMETRY. 150-154. Pythagorean Theorem. “MATHEMATICS II” - www.marlonrelles.com. to solve problems involving Pythagorean Theorem. “MATHEMATICS II” - www.marlonrelles.com. EOC REVIEW: Linear Functions. I DO (Teacher Only). “MATHEMATICS II” - www.marlonrelles.com.

301 views • 16 slides

TRIGONOMETRY. . Sign for sin  , cos  and tan . Quadrant II 90 ° <  < 180°. SIN  (+). ALL (+). Quadrant I 0 ° <  < 90°.  = 180 °− . Let  = acute angle.  = . . . . .  = 180 °+ .  = 360 °− . TAN  (+). COS  (+). Quadrant IV 270 ° <  < 360°.

387 views • 6 slides

TRIGONOMETRY. Find trigonometric ratios using right triangles Solve problems using trigonometric ratios. Sextant. TRIGONOMETRIC RATIOS. TRIGONOMETRY comes from two Greek terms: trigon , meaning triangle metron , meaning measure. TRIGONOMETRIC RATIOS.

449 views • 19 slides

Mathematics Presentation for Class 10

Mathematics, chapter 1: real number, chapter 2: polynomials, chapter 3: pair of linear equation in two variables, chapter 4: quadratic equations, chapter 5: arithmetic progressions, chapter 6: triangles, chapter 7: coordinate geometry, chapter 8: introduction to trigonometry, chapter 9: some applications of trigonometry, chapter 10: circles, chapter 11: constructions, chapter 12: areas related to circles, chapter 13: surface areas and volumes, chapter 14: statistics, chapter 15: probability.

Amazon Affiliate Disclaimer:    cbsecontent.com is a part of Amazon Services LLC Associates Program, an affiliate advertising program  designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.in. As an amazon associates we earn from qualifying purchases.

Some Application of Trigonometry Class 10 PPT

Top courses for class 10, faqs on some application of trigonometry class 10 ppt, mock tests for examination, extra questions, important questions, video lectures, practice quizzes, study material, shortcuts and tricks, sample paper, past year papers, objective type questions, previous year questions with solutions, semester notes, viva questions.

PPT: Some Application of Trigonometry Free PDF Download

Importance of ppt: some application of trigonometry, ppt: some application of trigonometry notes, ppt: some application of trigonometry class 10 questions, study ppt: some application of trigonometry on the app, welcome back, create your account for free.

Forgot Password

Unattempted tests, change country, practice & revise.

• Class 10 Maths
• Chapter 8: Introduction Trigonometry

Important Questions for Class 10 Maths Chapter 8- Introduction to Trigonometry

Important questions of Chapter 8 – Introduction to Trigonometry of Class 10 are given here for students who want to score high marks in their board exams 2022-2023. Students can also download the trigonometry class 10 questions pdf which is available on our website. They can learn and solve the problems offline by downloading trigonometry class 10 questions pdf.  The questions which are provided below are as per the latest CBSE syllabus and are designed according to the NCERT book. The questions are formulated after analyzing the previous year’s questions papers, exam trends and latest sample papers. Solving these questions will help students to get prepared for the final exam. Students can also get important questions for all the chapters of 10th standard Maths . Solve them to get acquainted with the various types of questions to be asked from each chapter of the Maths subject.

Also, get access to Class 10 Maths Chapter 8 Introduction to Trigonometry MCQs here.

In Chapter 8, students will be introduced to the Trigonometry concept, which states the relationship between angles and sides of a triangle. They will come across many trigonometric formulas which will be used to solve numerical problems. The six primary trigonometric ratios are sine, cosine, tangent, secant, cosecant and cotangent. The whole trigonometry concept revolves around these ratios or sometimes also called functions. Students can learn more about trigonometry class 10 questions, which are provided with complete explanations. Trigonometry Class 10 Maths Chapter 8 Important Questions are solved by our expert teachers so that students can understand the problems quickly. Besides, students can also get additional questions on chapter 8 of class 10 maths for practice at the end.

Class 10 Maths Chapter 8 Important Questions and Answers

Below are the important trigonometry class 10 questions. Students can refer to the below-given class 10 trigonometry questions and they can practice these problems as well.

Question. 1 : In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm.

Determine: (i) sin A, cos A (ii) sin C, cos C

In a given triangle ABC, right-angled at B = ∠B = 90°

Given: AB = 24 cm and BC = 7 cm

That means, AC = Hypotenuse

According to the Pythagoras Theorem,

In a right-angled triangle, the squares of the hypotenuse side are equal to the sum of the squares of the other two sides.

By applying the Pythagoras theorem, we get

AC 2  = AB 2  + BC 2

AC 2  = (24) 2  + 7 2

AC 2  = (576 + 49)

AC 2  = 625 cm 2

Therefore, AC = 25 cm

(i) We need to find Sin A and Cos A.

As we know, sine of the angle is equal to the ratio of the length of the opposite side and hypotenuse side. Therefore,

Sin A = BC/AC = 7/25

Again, the cosine of an angle is equal to the ratio of the adjacent side and hypotenuse side. Therefore,

cos A = AB/AC = 24/25

(ii) We need to find Sin C and Cos C.

Sin C = AB/AC = 24/25

Cos C = BC/AC = 7/25

Question 2: If Sin A = 3/4, Calculate cos A and tan A.

Solution: Let us say, ABC is a right-angled triangle, right-angled at B.

Sin A = 3/4

As we know,

Sin A = Opposite Side/Hypotenuse Side = 3/4

Now, let BC be 3k and AC will be 4k.

where k is the positive real number.

As per the Pythagoras theorem, we know;

Hypotenuse 2 = Perpendicular 2 + Base 2

AC 2 = AB 2 + BC 2

Substitute the value of AC and BC in the above expression to get;

(4k) 2 = (AB) 2 + (3k) 2

16k 2 – 9k 2 = AB 2

AB 2 = 7k 2

Hence, AB =  √7 k 

Now, as per the question, we need to find the value of cos A and tan A.

cos A = Adjacent Side/Hypotenuse side = AB/AC

cos A =  √7 k/4k = √7/4

tan A = Opposite side/Adjacent side = BC/AB

tan A = 3k/ √7 k = 3/√7

Question.3: If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B.

Suppose a triangle ABC, right-angled at C.

Now, we know the trigonometric ratios,

cos A = AC/AB

cos B = BC/AB

Since, it is given,

cos A = cos B

AC/AB = BC/AB

We know that by isosceles triangle theorem, the angles opposite to the equal sides are equal.

Therefore, ∠A = ∠B

Question 4: If 3 cot A = 4, check whether (1 – tan 2 A)/(1 + tan 2 A) = cos 2 A – sin 2 A or not.

Let us consider a triangle ABC, right-angled at B.

3 cot A = 4

cot A = 4/3

Since, tan A = 1/cot A

tan A = 1/(4/3) = 3/4

BC/AB = 3/4

Let BC = 3k and AB = 4k

By using Pythagoras theorem, we get;

AC 2 = (4k) 2 + (3k) 2

AC 2 = 16k 2  + 9k 2

AC = √ 25k 2  = 5k

sin A = Opposite side/Hypotenuse

In the same way,

cos A = Adjacent side/hypotenuse

To check: (1-tan 2 A)/(1+tan 2 A) = cos 2 A – sin 2 A or not

Let us take L.H.S. first;

= [1 – (9/16)]/[1 + (9/16)] = 7/25

R.H.S. = cos 2 A – sin 2 A = (4/5) 2  – (3/5) 2

= (16/25) – (9/25) = 7/25

L.H.S. = R.H.S.

Hence, proved.

Question 5: In triangle PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

Solution: Given,

In triangle PQR,

PR + QR = 25 cm

Let us say, QR = x

Then, PR = 25 – QR = 25 – x

Using Pythagoras theorem:

PR 2 = PQ 2 + QR 2

Now, substituting the value of PR, PQ and QR, we get;

(25 – x) 2 = (5) 2 + (x) 2

25 2  + x 2  – 50x = 25 + x 2

625 – 50x = 25

So, QR = 12 cm

PR = 25 – QR = 25 – 12 = 13 cm

sin P = QR/PR = 12/13

cos P = PQ/PR = 5/13

tan P = QR/PQ = 12/5

Question 6: Evaluate 2 tan 2 45° + cos 2 30° – sin 2 60°.

Solution: Since we know,

tan 45° = 1

cos 30° = √ 3/2

sin 60° = √ 3/2

Therefore, putting these values in the given equation:

2(1) 2 + ( √ 3/2) 2 – ( √ 3/2) 2

Question 7: If tan (A + B) =√3 and tan (A – B) =1/√3, 0° < A + B ≤ 90°; A > B, find A and B.

tan (A + B) = √3

As we know, tan 60° = √3

Thus, we can write;

⇒ tan (A + B) = tan 60°

⇒(A + B) = 60° …… (i)

Now again given;

tan (A – B) = 1/√3

Since, tan 30° = 1/√3

⇒ tan (A – B) = tan 30°

⇒(A – B) = 30° ….. (ii)

Adding the equation (i) and (ii), we get;

A + B + A – B = 60° + 30°

Now, put the value of A in eq. (i) to find the value of B;

45° + B = 60°

B = 60° – 45°

Therefore A = 45° and B = 15°

Question 8: Show that :

(i) tan 48° tan 23° tan 42° tan 67° = 1

(ii) cos 38° cos 52° – sin 38° sin 52° = 0

(i) tan 48° tan 23° tan 42° tan 67°

We can also write the above given tan functions in terms of cot functions, such as;

tan 48° = tan (90° – 42°) = cot 42°

tan 23° = tan (90° – 67°) = cot 67°

Hence, substituting these values, we get

= cot 42° cot 67° tan 42° tan 67°

= (cot 42° tan 42°) (cot 67° tan 67°)

(ii) cos 38° cos 52° – sin 38° sin 52°

We can also write the given cos functions in terms of sin functions.

cos 38° = cos (90° – 52°) = sin 52°

cos 52°= cos (90° – 38°) = sin 38°

Hence, putting these values in the given equation, we get;

sin 52° sin 38° – sin 38° sin 52° = 0

Question 9: If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.

tan 2A = cot (A – 18°)

As we know by trigonometric identities,

tan 2A = cot (90° – 2A)

Substituting the above equation in the given equation, we get;

⇒ cot (90° – 2A) = cot (A – 18°)

⇒ 90° – 2A = A – 18°

⇒ 108° = 3A

A = 108° / 3

Hence, the value of A = 36°

Question 10:  If A, B and C are interior angles of a triangle ABC, then show that sin [(B + C)/2] = cos A/2.

As we know, for any given triangle, the sum of all its interior angles is equals to 180°.

A + B + C = 180° ….(1)

Now we can write the above equation as;

⇒ B + C = 180° – A

Dividing by 2 on both the sides;

⇒ (B + C)/2 = (180° – A)/2

⇒ (B + C)/2 = 90° – A/2

Now, put sin function on both sides.

⇒ sin (B + C)/2 = sin (90° – A/2)

sin (90° – A/2) = cos A/2

sin (B + C)/2 = cos A/2

Question 11: Prove the identities:

(i) √[1 + sinA/1 – sinA] = sec A + tan A

(ii) (1 + tan 2 A/1 + cot 2 A) = (1 – tan A/1 – cot A) 2 = tan 2 A Solution: (i) Given:√[1 + sinA/1 – sinA] = sec A + tan A

LHS: = (1+tan²A) / (1+cot²A) Using the trigonometric identities we know that 1+tan²A = sec²A and 1+cot²A= cosec²A = sec²A/ cosec²A On taking the reciprocals we get = sin²A/cos²A = tan²A RHS: =(1-tanA)²/(1-cotA)² Substituting the reciprocal value of tan A and cot A we get, = (1-sinA/cosA)²/(1-cosA/sinA)² = [(cosA-sinA)/cosA]²/ [(sinA-cos)/sinA)²] = [(cosA-sinA)²×sin²A] /[cos²A. /(sinA-cosA)²] =  sin²A/cos²A = tan 2 A The values of LHS and RHS are the same. Hence proved.

Question 12: If sin θ + cos θ = √3, then prove that tan θ + cot θ = 1.

sin θ + cos θ = √3

Squaring on both sides,

(sin θ + cos θ) 2 = (√3) 2

sin 2 θ + cos 2 θ + 2 sin θ cos θ = 3

Using the identity sin 2 A + cos 2 A = 1,

1 + 2 sin θ cos θ = 3

2 sin θ cos θ = 3 – 1

2 sin θ cos θ = 2

sin θ cos θ = 1

sin θ cos θ = sin 2 θ + cos 2 θ

⇒ (sin 2 θ + cos 2 θ)/(sin θ cos θ) = 1

⇒ [sin 2 θ/(sin θ cos θ)] + [cos 2 θ/(sin θ cos θ)] = 1

⇒ (sin θ/cos θ) + (cos θ/sin θ) = 1

⇒ tan θ + cot θ = 1

Hence proved.

Question 13: Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

cot 85° + cos 75° 

= cot (90° – 5°) + cos (90° – 15°) 

We know that cos(90° – A) = sin A and cot(90° – A) = tan A

= tan 5° + sin 15°

Question 14: What is the value of (cos 2 67° – sin 2 23°)?

(cos 2 67° – sin 2 23°) = cos 2 (90° – 23°) – sin 2 23°

We know that cos(90° – A) = sin A

= sin 2 23° – sin 2 23°

Therefore, (cos 2 67° – sin 2 23°) = 1.

Question 15: Prove that (sin A – 2 sin 3 A)/(2 cos 3 A – cos A) = tan A.

LHS = (sin A – 2 sin 3 A)/(2 cos 3 A – cos A)

= [sin A(1 – 2 sin 2 A)]/ [cos A(2 cos 2 A – 1]

Using the identity sin 2 θ + cos 2 θ = 1,

= [sin A(sin 2 A + cos 2 A – 2 sin 2 A)]/ [cos A(2 cos 2 A – sin 2 A – cos 2 A]

= [sin A(cos 2 A – sin 2 A)]/ [cos A(cos 2 A – sin 2 A)]

= sin A/cos A

Also, check: Trigonometry Class 10 Questions PDF .

Video Lesson on Trigonometry

Introduction to Trigonometry Class 10 Questions for Practice

Solve the following class 10 Maths trigonometry problems:

• If sec θ + tan θ = 7, the compute the value of sec θ – tan θ
• If tan θ + cot θ = 5, then find the value of tan 2 θ + cot 2 θ.
• What will happen if the value of the cosine function increases from 0° to 90°?
• Given that cosec θ = 4/3. Find all other values of trigonometric ratios.
• Find the value of sin 45 °- Cos 45°.
• If 4 tan θ = 3, evaluate (4 sin θ – cos θ + 1)/(4 sin θ + cos θ + 1).
• Prove that [tan θ/(1 – cot θ)] + [cot θ/(1 – tan θ)] = 1 + sec θ cosec θ
• Prove that: sin θ/(cot θ + cosec θ) = 2 + [sin θ/ (cot θ – cosec θ]
• In a right triangle ABC, right-angled at B, if tan A = 1, then verify that 2 sin A cos A = 1.
• If ∠B and ∠Q are acute angles such that sin B = sin Q, then prove that ∠B = ∠Q.

We hope students must have found this information on Important Questions Class 10 Maths Chapter 8 Introduction to Trigonometry helpful for their board exam preparation. Stay tuned with BYJU’S – The Learning App and download the app to get all the chapter-wise important questions for class 10 Maths and also get the latest updates on the syllabus.

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

Please send me mail about the important question of maths

Nice work by byjus ..

It is very good work from byjus and this questions are very helpful for us

Good short and easy but important one’s

thank u soo much byju

These are easy, please upload most important and 100% asking questions in board

That’s very helpful to me during my exams. Thanks to BYJU’S App.

Thank you byjus. I was searching for trigonometry related this type questions only.

Thank you Byju’s the learning app,this is going to be much helpful for us Please upload more questions similar to this with a little bit more complexity. By the way, I am one of those Byju’s offline users, but yet searching in google for more questions Please upload the most important EXERCISE QUESTIONS and EXAMPLE QUESTIONS from textbook as well

Thank you Byju’s this helped me a lot in my internal assessments.

Thank you, BYJU’S ! It helped me a lot for my PRE-BOARD.

If cosec+ cot=k them prove that cos=k²-1/k²+1

Please refer: https://byjus.com/question-answer/if-cosec-theta-cot-theta-p-then-prove-that-cos-theta-frac-p-2-1/

• Share Share

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

• International
• Schools directory
• Resources Jobs Schools directory News Search

Trigonometry - Sequence of Lessons

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

6 July 2016

• Share through email
• Share through twitter
• Share through linkedin
• Share through facebook
• Share through pinterest

Tes classic free licence

Your rating is required to reflect your happiness.

It's good to leave some feedback.

Something went wrong, please try again later.

Empty reply does not make any sense for the end user

helen_f_mahony1

I love your ppt, they explain things well and are engaging. Thank you for sharing your ideas.

Brilliant! Just what I needed... Thank you!

anjana_nayyar2

thank you so much

Absolutely brilliant resource. Thank you so much!

Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch.

Not quite what you were looking for? Search by keyword to find the right resource:

• Preferences

On Trigonometry For Class 10 PowerPoint PPT Presentations