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Trigonometry Identities: A Comprehensive Guide for Math 185 Students, Cheat Sheet of Trigonometry

Santa Ana CollegeTrigonometry

Typology: Cheat Sheet

2020/2021

Uploaded on 04/26/2021

amritay
amritay 🇺🇸

4.7

(14)

256 documents

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Trigonometry Identities
Must have these memorized for Test and Final Exam
Ratio

 
sin tan
cos
uu
u
.

 
cos cot
sin
uu
u
Reciprocal
 
1sec
cos u
u
 
1csc
sin u
u
Pythagorean
 
 
22
22
22
cos sin 1
1tan sec
1cot csc
uu
uu
uu



Know the exact values of
sine, cosine, and tangent for
0, , , ,
6432

.Be able to
apply these to all the quadrants.
Sum/Difference

sin( ) sin cos cos sinAB A B A B

cos( ) cos cos sin sinAB A B A B

 
tan tan
tan( ) 1tan tan
AB
AB AB

Even/Odd Functions

cos( ) cos ( )u u even

sin( ) sin ( )u u odd

tan( ) tan ( )u u odd
Cofunctions



sin cos
2
tan cot
2
sc csc
2
uu
uu
eu u












Arc Length Sector Area
( in radians)
Sr
2
1r
2
A
Linear and Angular Velocities
,,
S
vwvrw
tt

Double Angle
 



 

22
2
2
2
sin 2 2sin cos
cos 2 cos sin
cos 2 2cos 1
cos 2 1 2sin
2tan
tan 2 1tan
uuu
uuu
uu
uu
u
uu



Half Angle




1cos
1
sin 22
1cos
1
cos 22
1cos
1
tan 21cos
v
v
v
v
v
vv












Area of a Triangle
For SAS: 1sin
2
A
ab C
For (SSS): ()()()Assasbsc ; where 1()
2
s abc

Law of Sines
  
side
sin sin sin sin(opp angle)
abc
ABC

.
Law of Cosines

222
2 cos abc bc A
222
(sd 1) (sd 2) (sd 3) 2(sd 2)(sd 3)cos(angle opp sd 1)
pf2

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Download Trigonometry Identities: A Comprehensive Guide for Math 185 Students and more Cheat Sheet Trigonometry in PDF only on Docsity!

Trigonometry Identities

Must have these memorized for Test and Final Exam

Ratio

 

 

 

sin tan cos

u u u

.

 

 

 

cos cot sin

u u u

Reciprocal

 

 

sec cos

u u

 

 

csc sin

u u

Pythagorean

   

   

   

2 2

2 2

2 2

cos sin 1

1 tan sec

1 cot csc

u u

u u

u u

Know the exact values of

sine, cosine, and tangent for

.Be able to

apply these to all the quadrants.

Sum/Difference

sin( AB )  sin (^)  A  (^) cos (^)  B (^)  cos (^)  A (^)  sin B

cos( AB )  cos (^)  A (^)  cos (^)  B (^)  sin (^)  A (^)  sin B

   

   

tan tan tan( ) 1 tan tan

A B

A B

A B

Even/Odd Functions

cos(  u ) cos (^)  u (^)  ( even )

sin(  u )  sin (^)  u (^)  ( odd )

tan(  u )  tan (^)  u (^)  ( odd )

Cofunctions

sin cos 2

tan cot 2

s c csc 2

u u

u u

e u u

 

 

 

Arc Length Sector Area

(  in radians)

S  r 

r 2

A  

Linear and Angular Velocities

v S , w , v r w t t

Double Angle

     

     

   

   

 

 

 

2 2

2

2

2

sin 2 2sin cos

cos 2 cos sin

cos 2 2cos 1

cos 2 1 2sin

2 tan tan 2 1 tan

u u u

u u u

u u

u u

u u u

 

 

 

 

Half Angle

1 1 cos sin 2 2

1 1 cos cos 2 2

1 1 cos tan 2 1 cos

v v v v v v v  ^      

       

         

Area of a Triangle

For SAS:

sin 2

Aab C

For (SSS): As s (  a )( sb )( sc ) ; where

sabc

Law of Sines

     

side

sin sin sin sin(opp angle)

a b c

A B C

.

Law of Cosines

 

2 2 2 abc  2 bc cos A

2 2 2 (sd 1)  (sd 2)  (sd 3) 2(sd 2)(sd 3)cos(angle opp sd 1)

No need to be memorized for Test and Final Exam

Math 185 students need to memorize Product to sum formulas

Product to Sum

sin sin cos cos 2

A B A B A B

cos cos cos cos 2

A B A B A B

sin cos sin sin 2

A B A B A B

Sum to Product

sin   sin   2 cos sin

A B A B

A B

 ^    

sin   sin   2sin cos

A B A B

A B

 ^    

cos   cos   2 cos cos

A B A B

A B

 ^    

cos   cos   2sin sin

A B A B

A B

 ^    

Majid Kashi