Trigonometric Identities Review

Identities

100

 csc x=

1 / (sin x)

200

(sin x) / (cos x)=

tan x?

300

1 / (sec x)=

cos x?

400

(cos x) / (sin x)=

cot x?

500

cos (-x)=

cos x

Simplifying Identities

100

(sec x)(cos x)=

1

200

(tan x)(cos x)=

sin x

300

(sec x) / (tan x)=

csc x

400

sin x (csc x - sec x)=

1 - tan x?

500

csc x - sin x=

(cos²x) / (sin x) OR (cos x)(cot x) ?

Pythagorean Identities

100

sin²x + cos²x=

1

200

1 + cot²x=

csc²x

300

1 - cos²x=

sin²x

400

sec²x - 1=

tan²x

500

(1 + csc x)(1 - csc x)=

-cot²x 

Solving Trig Equations

100

Solutions for 0 to 360 degrees for sin x = √3 / 2

60 and 120 degrees

200

Solutions of 0 to 360 for 2cosx +4=0

60 and 300 degrees

300

All solutions 0 to 360 degrees for 2sinx - 1 = 0

30 and 150 degrees

400

All solutions 0 to 360 for sin²x-2cosx-2=0 (Hint: Look at Trig Identities)

180 degrees

500

All solutions from 0 to 360 degrees for 5cosx- √3 = 3cosx

30 and 330 degrees