AP Calc BC - Trig Rules and Identities

d/dx (sinx)

cosx

d/dx (cosx)

-sinx

d/dx (tanx)

sec²x

d/dx (cotx)

-csc²x

d/dx (secx)

secxtanx

d/dx (cscx)

-cscxcotx

∫cosxdx

sinx + C

∫sinxdx

-cosx + C

∫sec²xdx

tanx + C

∫secxtanxdx

secx + C

∫cscxcotxdx

-cscx + C

∫csc²xdx

-cotx + C

∫tanxdx

-ln|cosx| + C or ln|secx| + C

∫secxdx

ln|secx + tanx| + C

∫cscxdx

ln|cscx - cotx| + C

sin2x

2sinxcosx

cos2x

cos²x - sin²x = 1 - 2sin²x = 2cos²x - 1

tan2x

2tanx/(1 - tan²x)

sin(x/2)

±√[(1 - cosx)/2]

cos(x/2)

±√[(1 + cosx)/2]

tan(x/2)

(1 - cosx)/sinx

sin²x + cos²x

1

tan²x + 1

sec²x

1 + cot²x

csc²x