# Trigonometry

By : Raghavendra Singh

Updated : Dec 28, 2020, 5:37

Trigonometry is one of the most important branches of mathematics and was first conceived by the Greek mathematician Hipparchus. It deals with the relationship between the three sides of a right-angled triangle which comprises of the base, hypotenuse, and perpendicular. For CAT aspirants, trigonometry is one of the most scoring topics that come under the Quantitative Aptitude section.

Trigonometry is defined by three primary functions - sine, cosine, and tangent. It helps in finding out missing angles and missing sides of a right-angled triangle, and the common angles in trigonometry that include 0°, 30°, 45°, 60°, and 90°. These angles are either measured in radians or degrees. These trigonometric functions also have their corollary counterparts. These are cosecant functions, secant functions, and cotangent functions.

Some important methods to calculate these functions are mentioned in the table below:

 Functions Abbreviation Explanation Sine Function sin It is the ratio of perpendicular over the hypotenuse of a right-angled triangle. Tangent Function tan It is the ratio of the perpendicular over the base of a right-angled triangle. Cosine Function cos It is the ratio of the base over the hypotenuse of a right-angled triangle. Cosecant Function cosec It is the ratio of hypotenuse over the perpendicular of a right-angled triangle. Secant Function sec It is the ratio of the hypotenuse over the base of a right-angled triangle. Cotangent Function cot It is the ratio of the base over the perpendicular of a right-angled triangle.

Once you are clear with the idea of the basic trigonometric functions, it is easy to work with its corollary as well. This is the first step to excelling in trigonometry for the CAT exam.

## Important Trigonometry Topics

Trigonometry is one of those topics of Mathematics where there is no end to a variety of questions that can be formed. However, the following important topics listed below will certainly help you solve the trigonometric equations.

1. Trigonometric/Pythagorean Identities

The Trigonometric Identities are trigonometry formulae that you can use to find out missing angles on a right-angled triangle. These are the formulae that are true in all cases in the case of Right-Angled Triangles. A few important trigonometric identities have been listed below:

2. Pythagorean Identities:

• sin²θ + cos²θ = 1
• tan²θ + 1 = sec²θ
• cot²θ + 1 = cosec²θ

3. Compound Angle Trigonometric Identities

After the trigonometric identities discussed above, you will come across a variation known as compound angles. This denotes the angles formed by more than one side of a right-angled triangle in trigonometry. This is perhaps the most important portion of trigonometry for the CAT Exam.

For angles u and v, we can derive the following relationships:

Sum of Angles:

• sin(u + v) = sin(u)cos(v) + cos(u)sin(v)
• cos(u + v) = cos(u)cos(v) – sin(u)sin(v)
• tan(u+v) = tan(u) + tan(v) or 1−tan(u) tan(v)

Difference of Angles:

• sin(u – v) = sin(u)cos(v) – cos(u)sin(v)
• cos(u – v) = cos(u)cos(v) + sin(u)sin(v)
• tan(u-v) = tan(u) − tan(v) or 1+tan(u) tan(v)

4. Sine and Cosine Laws:

Consider A, B and C to be the angles made by sides a, b and c of a right-angled triangle. In this case:

Sine Laws

• a/sinA = b/sinB = c/sinC

Cosine Laws

• c2 = a2 + b2 − 2ab cos(C)
• a2 = b2 + c2 − 2bc cos(A)
• b2 = a2 + c2 − 2ac cos(B)

5. Multiple Angle Theorem in Trigonometry

If you want to find out the trigonometric values corresponding to multiple angles made by a right-angledright angled triangle, you can use any of the following identities to do so.

• sin 2θ = 2 sin θ cos θ
• cos 2θ = cos²θ – sin²θ
• tan 2θ = 2 tan θ / (1 – tan²θ)
• cot 2θ = (cot²θ – 1) / 2 cot θ

6. Euler’s Law in Trigonometry

As per Euler’s law,

eix = cos x + i sin x

Where x is an angle subtended by the triangle and i is an imaginary number. Then,

Sin x=eix−e−ix2i

Cos x=eix+e−ix2

Tan x=(eix−e−ix) x i(eix+e−ix)

### Tips to Solve Trigonometry Questions for CAT

The following given tips will be handy when you solve the trigonometry question paper for CAT.

• Always start with the use of the basic trigonometric identities listed above.
• Try to break down all equations into the simplest forms with the use of trigonometric identities and mathematical formulae.
• Convert all corollaries to their original form. For instance, change cot to tan and cosecant to cosine functions wherever possible.
• Dedicate more time toward deducing the right way to solve a trigonometric equation first instead of directly jumping into the sum at large.
• Practice more and more types of trigonometric equations to get a hang of the real questions in the CAT exam. You can avail various short cut techniques this way as well.
• Do not spend too much time on one question as this will lead to a delay in the solving rest of the questions ahead.
• Do not answer a trigonometry question without attempting to solve it.

### Importance of Trigonometry in the Quantitative Section CAT Exams

Trigonometry is that branch of maths of which applications are used in our everyday lives.

• Trigonometry is one of the most scoring portions of the quantitative aptitude section in a CAT Exam.
• Trigonometric concepts help understand your grasp of basic logical and mathematical theorems.
• Trigonometry is a discipline where guesswork does not bring out positive results. It is so because all the answers are seemingly similar to each other. This tests the candidate’s real aptitude in the field.
• Trigonometry helps candidates identify with right-angled triangles and gain conceptual clarity in triangular geometry and angle measurements.

## Most Recommended Books for Trigonometry in CAT Exam

We have listed some of the widely used books for the preparation of the quantitative aptitude section of CAT.

 Name Author/Publisher Description Lucent’s Higher Mathematics Part 2 Rishikesh Kumar This is one of the best books to practice trigonometry for all competitive exams including CAT and other MBA Entrance tests, SSC, banking. It comprises various types of well-illustrated examples and short cut techniques. The focus is on concepts rather than MCQ questions. It is available in paperback format. Essential Trigonometry: A Self-Teaching Guide Tim Hill, McGraw Hill You can clear out all your concepts and practice various types of sums with this book's help. It is a paperback book that is written made in a manner to help you learn self by yourself.

## Why prepare Trigonometry from BYJU'S Exam Prep?

BYJU'S Exam Prep is an online exam preparation platform with a simplistic user experience. It is perfect for preparing for major competitive exams such as CAT, XAT, SSC, etc. BYJU'S Exam Prep provides its students with the following benefits for the candidates who are preparing for CAT Exam.

• CAT Live classes
• Easy interaction with the experts and faculties
• Daily MCQ quizzes for CAT
• CAT Practice Tests
• CAT Mock Tests
• CAT Previous year question papers with the latest one as well
• Doubt clearing on a discussion board
• Well scheduled preparation strategy

### FAQs

1.What is trigonometry?

Trigonometry is a part of mathematics that deals with measuring the missing angles of a right-angled triangle. The most common degrees used in trigonometry include 0°, 30°, 45°, 60°, and 90°.

2. What is a tangent?

Tangent or tan A is the measure of the ratio of the sine and cosine of angle A. In other words, if A is the angle subtended by the perpendicular and base, then the tangent is tan A.

3. What is the Pythagorean trigonometric formulae?

The three Pythagorean trigonometric identities are:

sin²θ + cos²θ = 1, tan²θ + 1 = sec²θ and cot²θ + 1 = cosec²θ

4. What are topics under trigonometry for the CAT Exam?

The important topics under trigonometry for CAT exam are:-

• Pythagorean Identities
• Sine and Cosine Laws
• Multiple Angle and Sub Multiple Angle Theorem
• Submultiple Angle Theorem
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