Trig Identities

Math 131 Trig Identities and Derivatives

d/dx sin(x)

cos(x)

d/dx cos(x)

-sin(x)

d/dx tan(x)

sec²(x)

d/dx csc(x)

-csc(x)cot(x)

d/dx sec(x)

sec(x)tan(x)

d/dx cot(x)

-csc²(x)

sinθ

O/H

cosθ

A/H

tanθ

O/A

cscθ = 1/sinθ

H/O

secθ = 1/cosθ

H/A

cotθ = 1/tanθ & cosθ/sinθ

A/O

tan^-1(x)

arctan(x)

sin^-1(x)

arcsin(x)

d/dx arctan(x)

1/1+x²

d/dx arcsin(x)

1/sqrt(1-x²)

sin²θ + cos²θ

1

1 + tan²θ

sec²θ