Identities for Evil evil Precalculus

This class is so confusing and Mr. Collins lowkey evil for not letting us use a cheat sheet

Reciprocal Identity: sinx

1/csc

Reciprocal Identity: cscx

1/sin

Reciprocal Identity: tanx

1/cot

Reciprocal Identity: cosx

1/sec

Reciprocal Identity: secx

1/cos

Reciprocal Identity: cotx

1/tan

Quotient Identity: tanx

sin/cos

Quotient Identity: cotx

cos/sin

Cofunction Identity: sinx

cos (π/2 - x)

Cofunction Identity: cosx

sin (π/2 - x)

Cofunction Identity: secx

csc (π/2 - x)

Cofunction Identity: cscx

sec (π/2 - x)

Even Identity: cos(-x)

cosx

Even Identity: sec(-x)

secx

Odd Identity: sin(-x)

-sinx

Odd Identity: csc(-x)

-cscx

Odd Identity: tan(-x)

-tanx

Odd Identity: cot(-x)

-cotx

Pythagorean Identity: cosx² + sinx²

1

Pythagorean Identity: tanx² + 1

secx²

Pythagorean Identity: cotx² + 1

cscx²

What is an Identity?

An equation that is always true

What is the purpose of identities?

To rewrite functions to make them graphable

Double Angle Identity: sin(2x)

2(sinxcosx)

Double Angle Identity: cos(2x)

cosx² - sinx²

Sum Identity: sin(a+b)

sinacosb + cosasinb

Sum Identity: cos(a+b)

cosacosb - sinasinb

Sum Identity: tan(a+b)

sin(a+b) / cos(a+b)