Pre-Calc Chapter 5 Identities

Reciprocal Identities

sinu =

1/cscu

cosu =

1/secu

tanu =

1/cotu

cscu =

1/sinu

secu =

1/cosu

cotu =

1/tanu

Pythagorean Identities

sin²u+cos²u =

1

sin²u =

1-cos²u

cos²u =

1-sin²u

tan²u+1 =

sec²u

tan²u =

sec²u - 1

1 =

sec²u - tan²u

1 + cot²u =

csc²u

1 =

csc²u - cot²u

cot²u =

csc²u-1

Co-Function Identities

sinθ =

cos(π/2-θ)

cosθ =

sin(π/2-θ)

tanθ =

cot(π/2-θ)

cscθ =

sec(π/2-θ)

secθ =

csc(π/2-θ)

cotθ =

tan(π/2-θ)

Even/ Odd Identities

sin(-θ) =

-sinθ

csc(-θ) =

-cscθ

tan(-θ) =

-tanθ

cot(-θ)

-cotθ

cos(-θ) =

cosθ

sec(-θ) =

secθ

Trig Memory Values (just to refresh)

cos30⁰ =

√3/2

cos60⁰ =

1/2

tan30⁰ =

1/√3

sin60⁰ =

√3/2

sin30° =

1/2

cot60° =

1/√3

Sum and Difference Formulas

sin(u + v) =

sinu cosv + cosu sinv

sin(u - v) =

sinu cosv - cosu sinv

cos(u + v) =

cosu cosv - sinu sinv

cos(u - v) =

cosu cosv + sinu sinv

tan(u + v) =

tanu + tannv/ 1 - tanu tanv

tan(u - v) =

tanu - tannv/ 1 + tanu tanv

Double Angle Formulas

sin2x =

2sinx cosx

tan2x =

2tanx/1-tan²x

cos2x =

cos²x - sin²x

cos2x =

1 - 2sin²x

cos2x =

2cos²x - 1

Power Reducing Formulas

sin²x =

1-cos2x/ 2

cos²x =

1 + cos2x/2

tan²x

1- cos2x/1+cos2x