Trig Identities Review

Trig Identities

100

Equal to 1/sinx

What is cscx ?

200

Equal to 1 + tan²x

What is sec²x ?

300

Equal to 1 - cos²x

What is sin²x ?

400

Equal to 1 + (cos²x / sin²x)

What is csc²x ?

500

sin²x-1

-cos²x

Trig Equations

100

Find all radian solutions of tan²x = 1

What are pi/4 + (pi/2)n ?

200

Find all radian solutions of tan(2x) = 1 in the interval [0, 2pi).

What are pi/8, 5pi/8, 9pi/8, 13pi/8 ?

300

Find all radian solutions of 2cos²x + cosx - 1 = 0 in the interval [0, 2pi).

What are pi/3, 5pi/3, and pi ?

400

Find all radian solutions of 2cos²x + cosx - 1 = 0

What are pi/3 + (2pi)n, 5pi/3 + (2pi)n, and pi + (2pi)n?

500

Solve 2sin²x=2+cosx on the interval [0,2pi)

pi/2, 3pi/2, 2pi/3, 4pi/3

Double and Half Angle Identities

100

The exact value of sin(15^o). 

What is (sqrt6 - sqrt2)/4 ?

200

The exact value of cos(75⁰). 

What is (sqrt 6 - sqrt 2)/4 ?

300

The exact value of sin(2x) if cosx = 1/4 and x is in quadrant 4.  

What is (- sqrt 15)/8 ?

400

The exact value of cos630^o. 

What is 0?

500

Find sin(u/2) when tanu=-5/12 and 3pi/2<u<2pi

sin(u/2)=square root 26/26

Factoring Trig Expressions

100

Factored form of sinxcosx + sinx

What is sinx(cosx + 1) ?

200

Factored form of tan²x - 2tanx - 3

What is (tanx - 3)(tanx + 1) ?

300

Factored form of cosxsin²x - cosxtan²x

What is cosx(sinx + tanx)(sinx - tanx)

400

Factored form of cos³x+ sin³x

What is (cosx + sinx)(-cosxsinx) ?

500

Factored form of cot² x + csc x -1

(cscx-1)(cscx+2)