Open App

JEE Exam > JEE Notes > Mathematics (Maths) for JEE Main & Advanced > Important Formulas & Examples: Trigonometric Functions - 1

Important Formulas & Examples: Trigonometric Functions - 1 | Mathematics (Maths) for JEE Main & Advanced PDF Download

Download, print and study this document offline

Please wait while the PDF view is loading

 Page 1


Trigonometric Formula Sheet
De?nition of the Trig Functions
Right Triangle De?nition
Assume that:
0 < ? <
? 2
or 0
 < ? < 90
 hypotenuse
adjacent
opposite
? sin? =
opp
hyp
csc? =
hyp
opp
cos? =
adj
hyp
sec? =
hyp
adj
tan? =
opp
adj
cot? =
adj
opp
Unit Circle De?nition
Assume ? can be any angle.
x
y
y
x
1
(x,y)
? sin? =
y
1
csc? =
1
y
cos? =
x
1
sec? =
1
x
tan? =
y
x
cot? =
x
y
Domains of the Trig Functions
sin? , 8 ? 2 (1 ,1 )
cos? , 8 ? 2 (1 ,1 )
tan? , 8 ? 6=
?
n+
1
2
?
? ,wheren2 Z
csc? , 8 ? 6= n? ,wheren2 Z
sec? , 8 ? 6=
?
n+
1
2
?
? ,wheren2 Z
cot? , 8 ? 6= n? ,wheren2 Z
Ranges of the Trig Functions
 1? sin? ? 1
 1? cos? ? 1
1? tan? ?1
csc?  1 and csc? ? 1
sec?  1 and sec? ? 1
1? cot? ?1
Periods of the Trig Functions
The period of a function is the number, T, such that f (? +T ) = f (? ).
So, if ! is a ?xed number and ? is any angle we have the following periods.
sin(!? ) ) T =
2? !
cos(!? ) ) T =
2? !
tan(!? ) ) T =
? !
csc(!? ) ) T =
2? !
sec(!? ) ) T =
2? !
cot(!? ) ) T =
? !
1
Page 2


Trigonometric Formula Sheet
De?nition of the Trig Functions
Right Triangle De?nition
Assume that:
0 < ? <
? 2
or 0
 < ? < 90
 hypotenuse
adjacent
opposite
? sin? =
opp
hyp
csc? =
hyp
opp
cos? =
adj
hyp
sec? =
hyp
adj
tan? =
opp
adj
cot? =
adj
opp
Unit Circle De?nition
Assume ? can be any angle.
x
y
y
x
1
(x,y)
? sin? =
y
1
csc? =
1
y
cos? =
x
1
sec? =
1
x
tan? =
y
x
cot? =
x
y
Domains of the Trig Functions
sin? , 8 ? 2 (1 ,1 )
cos? , 8 ? 2 (1 ,1 )
tan? , 8 ? 6=
?
n+
1
2
?
? ,wheren2 Z
csc? , 8 ? 6= n? ,wheren2 Z
sec? , 8 ? 6=
?
n+
1
2
?
? ,wheren2 Z
cot? , 8 ? 6= n? ,wheren2 Z
Ranges of the Trig Functions
 1? sin? ? 1
 1? cos? ? 1
1? tan? ?1
csc?  1 and csc? ? 1
sec?  1 and sec? ? 1
1? cot? ?1
Periods of the Trig Functions
The period of a function is the number, T, such that f (? +T ) = f (? ).
So, if ! is a ?xed number and ? is any angle we have the following periods.
sin(!? ) ) T =
2? !
cos(!? ) ) T =
2? !
tan(!? ) ) T =
? !
csc(!? ) ) T =
2? !
sec(!? ) ) T =
2? !
cot(!? ) ) T =
? !
1
Page 3


Trigonometric Formula Sheet
De?nition of the Trig Functions
Right Triangle De?nition
Assume that:
0 < ? <
? 2
or 0
 < ? < 90
 hypotenuse
adjacent
opposite
? sin? =
opp
hyp
csc? =
hyp
opp
cos? =
adj
hyp
sec? =
hyp
adj
tan? =
opp
adj
cot? =
adj
opp
Unit Circle De?nition
Assume ? can be any angle.
x
y
y
x
1
(x,y)
? sin? =
y
1
csc? =
1
y
cos? =
x
1
sec? =
1
x
tan? =
y
x
cot? =
x
y
Domains of the Trig Functions
sin? , 8 ? 2 (1 ,1 )
cos? , 8 ? 2 (1 ,1 )
tan? , 8 ? 6=
?
n+
1
2
?
? ,wheren2 Z
csc? , 8 ? 6= n? ,wheren2 Z
sec? , 8 ? 6=
?
n+
1
2
?
? ,wheren2 Z
cot? , 8 ? 6= n? ,wheren2 Z
Ranges of the Trig Functions
 1? sin? ? 1
 1? cos? ? 1
1? tan? ?1
csc?  1 and csc? ? 1
sec?  1 and sec? ? 1
1? cot? ?1
Periods of the Trig Functions
The period of a function is the number, T, such that f (? +T ) = f (? ).
So, if ! is a ?xed number and ? is any angle we have the following periods.
sin(!? ) ) T =
2? !
cos(!? ) ) T =
2? !
tan(!? ) ) T =
? !
csc(!? ) ) T =
2? !
sec(!? ) ) T =
2? !
cot(!? ) ) T =
? !
1
Identities and Formulas
Tangent and Cotangent Identities
tan? =
sin? cos? cot? =
cos? sin? Reciprocal Identities
sin? =
1
csc? csc? =
1
sin? cos? =
1
sec? sec? =
1
cos? tan? =
1
cot? cot? =
1
tan? Pythagorean Identities
sin
2
? +cos
2
? =1
tan
2
? +1=sec
2
? 1+cot
2
? =csc
2
? Even and Odd Formulas
sin( ? )= sin? cos( ? )=cos? tan( ? )= tan? csc( ? )= csc? sec( ? )=sec? cot( ? )= cot? Periodic Formulas
If n is an integer
sin(? +2? n) = sin? cos(? +2? n)=cos? tan(? +? n)=tan? csc(? +2? n)=csc? sec(? +2? n)=sec? cot(? +? n)=cot? Double Angle Formulas
sin(2? )=2sin? cos? cos(2? )=cos
2
?  sin
2
? =2cos
2
?  1
=1 2sin
2
? tan(2? )=
2tan? 1 tan
2
? Degrees to Radians Formulas
If x is an angle in degrees and t is an angle in
radians then:
? 180
 =
t
x
) t =
? x
180
 and x =
180
 t
? Half Angle Formulas
sin? =±
r
1 cos(2? )
2
cos? =±
r
1+cos(2? )
2
tan? =±
s
1 cos(2? )
1+cos(2? )
Sum and Di? erence Formulas
sin(? ± )=sin? cos ±cos? sin cos(? ± )=cos? cos ? sin? sin tan(? ± )=
tan? ±tan 1? tan? tan Product to Sum Formulas
sin? sin =
1
2
[cos(?   ) cos(? + )]
cos? cos =
1
2
[cos(?   )+cos(? + )]
sin? cos =
1
2
[sin(? + )+sin(?   )]
cos? sin =
1
2
[sin(? + ) sin(?   )]
Sum to Product Formulas
sin? +sin =2sin
?
? + 2
?
cos
?
?   2
?
sin?  sin =2cos
?
? + 2
?
sin
?
?   2
?
cos? +cos =2cos
?
? + 2
?
cos
?
?   2
?
cos?  cos = 2sin
?
? + 2
?
sin
?
?   2
?
Cofunction Formulas
sin
?
? 2
 ? ?
=cos? csc
?
? 2
 ? ?
=sec? tan
?
? 2
 ? ?
=cot? cos
?
? 2
 ? ?
=sin? sec
?
? 2
 ? ?
=csc? cot
?
? 2
 ? ?
=tan? 2
Page 4


Trigonometric Formula Sheet
De?nition of the Trig Functions
Right Triangle De?nition
Assume that:
0 < ? <
? 2
or 0
 < ? < 90
 hypotenuse
adjacent
opposite
? sin? =
opp
hyp
csc? =
hyp
opp
cos? =
adj
hyp
sec? =
hyp
adj
tan? =
opp
adj
cot? =
adj
opp
Unit Circle De?nition
Assume ? can be any angle.
x
y
y
x
1
(x,y)
? sin? =
y
1
csc? =
1
y
cos? =
x
1
sec? =
1
x
tan? =
y
x
cot? =
x
y
Domains of the Trig Functions
sin? , 8 ? 2 (1 ,1 )
cos? , 8 ? 2 (1 ,1 )
tan? , 8 ? 6=
?
n+
1
2
?
? ,wheren2 Z
csc? , 8 ? 6= n? ,wheren2 Z
sec? , 8 ? 6=
?
n+
1
2
?
? ,wheren2 Z
cot? , 8 ? 6= n? ,wheren2 Z
Ranges of the Trig Functions
 1? sin? ? 1
 1? cos? ? 1
1? tan? ?1
csc?  1 and csc? ? 1
sec?  1 and sec? ? 1
1? cot? ?1
Periods of the Trig Functions
The period of a function is the number, T, such that f (? +T ) = f (? ).
So, if ! is a ?xed number and ? is any angle we have the following periods.
sin(!? ) ) T =
2? !
cos(!? ) ) T =
2? !
tan(!? ) ) T =
? !
csc(!? ) ) T =
2? !
sec(!? ) ) T =
2? !
cot(!? ) ) T =
? !
1
Identities and Formulas
Tangent and Cotangent Identities
tan? =
sin? cos? cot? =
cos? sin? Reciprocal Identities
sin? =
1
csc? csc? =
1
sin? cos? =
1
sec? sec? =
1
cos? tan? =
1
cot? cot? =
1
tan? Pythagorean Identities
sin
2
? +cos
2
? =1
tan
2
? +1=sec
2
? 1+cot
2
? =csc
2
? Even and Odd Formulas
sin( ? )= sin? cos( ? )=cos? tan( ? )= tan? csc( ? )= csc? sec( ? )=sec? cot( ? )= cot? Periodic Formulas
If n is an integer
sin(? +2? n) = sin? cos(? +2? n)=cos? tan(? +? n)=tan? csc(? +2? n)=csc? sec(? +2? n)=sec? cot(? +? n)=cot? Double Angle Formulas
sin(2? )=2sin? cos? cos(2? )=cos
2
?  sin
2
? =2cos
2
?  1
=1 2sin
2
? tan(2? )=
2tan? 1 tan
2
? Degrees to Radians Formulas
If x is an angle in degrees and t is an angle in
radians then:
? 180
 =
t
x
) t =
? x
180
 and x =
180
 t
? Half Angle Formulas
sin? =±
r
1 cos(2? )
2
cos? =±
r
1+cos(2? )
2
tan? =±
s
1 cos(2? )
1+cos(2? )
Sum and Di? erence Formulas
sin(? ± )=sin? cos ±cos? sin cos(? ± )=cos? cos ? sin? sin tan(? ± )=
tan? ±tan 1? tan? tan Product to Sum Formulas
sin? sin =
1
2
[cos(?   ) cos(? + )]
cos? cos =
1
2
[cos(?   )+cos(? + )]
sin? cos =
1
2
[sin(? + )+sin(?   )]
cos? sin =
1
2
[sin(? + ) sin(?   )]
Sum to Product Formulas
sin? +sin =2sin
?
? + 2
?
cos
?
?   2
?
sin?  sin =2cos
?
? + 2
?
sin
?
?   2
?
cos? +cos =2cos
?
? + 2
?
cos
?
?   2
?
cos?  cos = 2sin
?
? + 2
?
sin
?
?   2
?
Cofunction Formulas
sin
?
? 2
 ? ?
=cos? csc
?
? 2
 ? ?
=sec? tan
?
? 2
 ? ?
=cot? cos
?
? 2
 ? ?
=sin? sec
?
? 2
 ? ?
=csc? cot
?
? 2
 ? ?
=tan? 2
Unit Circle
0
 ,2? (1,0)
180
 ,? ( 1,0)
(0,1)
90
 ,
? 2
(0, 1)
270
 ,
3? 2
30
 ,
? 6
(
p 3
2
,
1
2
)
45
 ,
? 4
(
p 2
2
,
p 2
2
)
60
 ,
? 3
(
1
2
,
p 3
2
)
120
 ,
2? 3
( 1
2
,
p 3
2
)
135
 ,
3? 4
( p 2
2
,
p 2
2
)
150
 ,
5? 6
( p 3
2
,
1
2
)
210
 ,
7? 6
( p 3
2
, 1
2
)
225
 ,
5? 4
( p 2
2
, p 2
2
)
240
 ,
4? 3
( 1
2
, p 3
2
)
300
 ,
5? 3
(
1
2
, p 3
2
)
315
 ,
7? 4
(
p 2
2
, p 2
2
)
330
 ,
11? 6
(
p 3
2
, 1
2
)
For any ordered pair on the unit circle (x,y):cos? = x and sin? = y
Example
cos(
7? 6
)= p 3
2
sin(
7? 6
)= 1
2
3
Page 5


Trigonometric Formula Sheet
De?nition of the Trig Functions
Right Triangle De?nition
Assume that:
0 < ? <
? 2
or 0
 < ? < 90
 hypotenuse
adjacent
opposite
? sin? =
opp
hyp
csc? =
hyp
opp
cos? =
adj
hyp
sec? =
hyp
adj
tan? =
opp
adj
cot? =
adj
opp
Unit Circle De?nition
Assume ? can be any angle.
x
y
y
x
1
(x,y)
? sin? =
y
1
csc? =
1
y
cos? =
x
1
sec? =
1
x
tan? =
y
x
cot? =
x
y
Domains of the Trig Functions
sin? , 8 ? 2 (1 ,1 )
cos? , 8 ? 2 (1 ,1 )
tan? , 8 ? 6=
?
n+
1
2
?
? ,wheren2 Z
csc? , 8 ? 6= n? ,wheren2 Z
sec? , 8 ? 6=
?
n+
1
2
?
? ,wheren2 Z
cot? , 8 ? 6= n? ,wheren2 Z
Ranges of the Trig Functions
 1? sin? ? 1
 1? cos? ? 1
1? tan? ?1
csc?  1 and csc? ? 1
sec?  1 and sec? ? 1
1? cot? ?1
Periods of the Trig Functions
The period of a function is the number, T, such that f (? +T ) = f (? ).
So, if ! is a ?xed number and ? is any angle we have the following periods.
sin(!? ) ) T =
2? !
cos(!? ) ) T =
2? !
tan(!? ) ) T =
? !
csc(!? ) ) T =
2? !
sec(!? ) ) T =
2? !
cot(!? ) ) T =
? !
1
Identities and Formulas
Tangent and Cotangent Identities
tan? =
sin? cos? cot? =
cos? sin? Reciprocal Identities
sin? =
1
csc? csc? =
1
sin? cos? =
1
sec? sec? =
1
cos? tan? =
1
cot? cot? =
1
tan? Pythagorean Identities
sin
2
? +cos
2
? =1
tan
2
? +1=sec
2
? 1+cot
2
? =csc
2
? Even and Odd Formulas
sin( ? )= sin? cos( ? )=cos? tan( ? )= tan? csc( ? )= csc? sec( ? )=sec? cot( ? )= cot? Periodic Formulas
If n is an integer
sin(? +2? n) = sin? cos(? +2? n)=cos? tan(? +? n)=tan? csc(? +2? n)=csc? sec(? +2? n)=sec? cot(? +? n)=cot? Double Angle Formulas
sin(2? )=2sin? cos? cos(2? )=cos
2
?  sin
2
? =2cos
2
?  1
=1 2sin
2
? tan(2? )=
2tan? 1 tan
2
? Degrees to Radians Formulas
If x is an angle in degrees and t is an angle in
radians then:
? 180
 =
t
x
) t =
? x
180
 and x =
180
 t
? Half Angle Formulas
sin? =±
r
1 cos(2? )
2
cos? =±
r
1+cos(2? )
2
tan? =±
s
1 cos(2? )
1+cos(2? )
Sum and Di? erence Formulas
sin(? ± )=sin? cos ±cos? sin cos(? ± )=cos? cos ? sin? sin tan(? ± )=
tan? ±tan 1? tan? tan Product to Sum Formulas
sin? sin =
1
2
[cos(?   ) cos(? + )]
cos? cos =
1
2
[cos(?   )+cos(? + )]
sin? cos =
1
2
[sin(? + )+sin(?   )]
cos? sin =
1
2
[sin(? + ) sin(?   )]
Sum to Product Formulas
sin? +sin =2sin
?
? + 2
?
cos
?
?   2
?
sin?  sin =2cos
?
? + 2
?
sin
?
?   2
?
cos? +cos =2cos
?
? + 2
?
cos
?
?   2
?
cos?  cos = 2sin
?
? + 2
?
sin
?
?   2
?
Cofunction Formulas
sin
?
? 2
 ? ?
=cos? csc
?
? 2
 ? ?
=sec? tan
?
? 2
 ? ?
=cot? cos
?
? 2
 ? ?
=sin? sec
?
? 2
 ? ?
=csc? cot
?
? 2
 ? ?
=tan? 2
Unit Circle
0
 ,2? (1,0)
180
 ,? ( 1,0)
(0,1)
90
 ,
? 2
(0, 1)
270
 ,
3? 2
30
 ,
? 6
(
p 3
2
,
1
2
)
45
 ,
? 4
(
p 2
2
,
p 2
2
)
60
 ,
? 3
(
1
2
,
p 3
2
)
120
 ,
2? 3
( 1
2
,
p 3
2
)
135
 ,
3? 4
( p 2
2
,
p 2
2
)
150
 ,
5? 6
( p 3
2
,
1
2
)
210
 ,
7? 6
( p 3
2
, 1
2
)
225
 ,
5? 4
( p 2
2
, p 2
2
)
240
 ,
4? 3
( 1
2
, p 3
2
)
300
 ,
5? 3
(
1
2
, p 3
2
)
315
 ,
7? 4
(
p 2
2
, p 2
2
)
330
 ,
11? 6
(
p 3
2
, 1
2
)
For any ordered pair on the unit circle (x,y):cos? = x and sin? = y
Example
cos(
7? 6
)= p 3
2
sin(
7? 6
)= 1
2
3

	Mathematics (Maths) for JEE Main & Advanced 209 videos\|443 docs\|143 tests

Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

Join Course for Free

Top Courses for JEE

View all

Related Exams

JEE

About this Document

	1.3K Views
	4.83/5 Rating
	Dec 22, 2024 Last updated

Document Description: Important Formulas & Examples: Trigonometric Functions - 1 for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The notes and questions for Important Formulas & Examples: Trigonometric Functions - 1 have been prepared according to the JEE exam syllabus. Information about Important Formulas & Examples: Trigonometric Functions - 1 covers topics like and Important Formulas & Examples: Trigonometric Functions - 1 Example, for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Important Formulas & Examples: Trigonometric Functions - 1.

Introduction of Important Formulas & Examples: Trigonometric Functions - 1 in English is available as part of our Mathematics (Maths) for JEE Main & Advanced for JEE & Important Formulas & Examples: Trigonometric Functions - 1 in Hindi for Mathematics (Maths) for JEE Main & Advanced course. Download more important topics related with notes, lectures and mock test series for JEE Exam by signing up for free. JEE: Important Formulas & Examples: Trigonometric Functions - 1 | Mathematics (Maths) for JEE Main & Advanced

Description

Full syllabus notes, lecture & questions for Important Formulas & Examples: Trigonometric Functions - 1 | Mathematics (Maths) for JEE Main & Advanced - JEE | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) for JEE Main & Advanced | Best notes, free PDF download

Information about Important Formulas & Examples: Trigonometric Functions - 1

In this doc you can find the meaning of Important Formulas & Examples: Trigonometric Functions - 1 defined & explained in the simplest way possible. Besides explaining types of Important Formulas & Examples: Trigonometric Functions - 1 theory, EduRev gives you an ample number of questions to practice Important Formulas & Examples: Trigonometric Functions - 1 tests, examples and also practice JEE tests

	Mathematics (Maths) for JEE Main & Advanced 209 videos\|443 docs\|143 tests

Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

Join Course for Free

Download as PDF

Explore Courses for JEE exam

Top Courses for JEE

Explore Courses

Signup for Free!

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.

Start learning for Free

10M+ students study on EduRev

Free

past year papers

shortcuts and tricks

Extra Questions

Important questions

Exam

pdf

study material

Viva Questions

Semester Notes

Important Formulas & Examples: Trigonometric Functions - 1 | Mathematics (Maths) for JEE Main & Advanced

mock tests for examination

Sample Paper

Objective type Questions

Important Formulas & Examples: Trigonometric Functions - 1 | Mathematics (Maths) for JEE Main & Advanced

practice quizzes

Summary

ppt

MCQs

video lectures

Important Formulas & Examples: Trigonometric Functions - 1 | Mathematics (Maths) for JEE Main & Advanced

Previous Year Questions with Solutions

;

Additional Information about Important Formulas & Examples: Trigonometric Functions - 1 for JEE Preparation

Important Formulas & Examples: Trigonometric Functions - 1 Free PDF Download

The Important Formulas & Examples: Trigonometric Functions - 1 is an invaluable resource that delves deep into the core of the JEE exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the Important Formulas & Examples: Trigonometric Functions - 1 now and kickstart your journey towards success in the JEE exam.

Importance of Important Formulas & Examples: Trigonometric Functions - 1

The importance of Important Formulas & Examples: Trigonometric Functions - 1 cannot be overstated, especially for JEE aspirants. This document holds the key to success in the JEE exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

Important Formulas & Examples: Trigonometric Functions - 1 Notes

Important Formulas & Examples: Trigonometric Functions - 1 Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to Important Formulas & Examples: Trigonometric Functions - 1. It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, Important Formulas & Examples: Trigonometric Functions - 1 Notes on EduRev are your ultimate resource for success.

Important Formulas & Examples: Trigonometric Functions - 1 JEE Questions

The "Important Formulas & Examples: Trigonometric Functions - 1 JEE Questions" guide is a valuable resource for all aspiring students preparing for the JEE exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study Important Formulas & Examples: Trigonometric Functions - 1 on the App

Students of JEE can study Important Formulas & Examples: Trigonometric Functions - 1 alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the Important Formulas & Examples: Trigonometric Functions - 1, students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of Important Formulas & Examples: Trigonometric Functions - 1 is prepared as per the latest JEE syllabus.

Education Revolution