Trig Identities

Math 131 Trig Identities and Derivatives + Math 132 Trig Integrals

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

1 + cot²θ

csc²θ

cos(2θ)

cos²θ - sin²θ

∫ sin(x) dx

-cos(x) + C

∫ cos(x) dx

sin(x) + C

∫ sec²(x) dx

tan(x) + C

∫ csc²(x) dx

-cot(x) +C

∫ sec(x)tan(x) dx

sec(x) + C

∫ csc(x)cot(x) dx

-csc(x) + C

∫ sec(x) dx

ln|sec(x) + tan(x)| + C

∫ csc(x) dx

ln|csc(x) - cot(x)| + C

∫ tan(x) dx

ln|sec(x)| + C

∫ cot(x) dx

ln|sin(x)| + C

∫ secθ dθ

ln|secθ + tanθ| + C

∫ cscθ dθ

ln|cscθ + cotθ| + C

∫ 1/(x²+a²)dx

1/a arctan(x/a) + C