Derivation and Integration of Trigonometric Functions

the ONE THING you gotta memorize for that ap calc ab (maybe bc too? idk im only in ab rn) exam

ƒ(x) = sin(x)

ƒ’(x) = cos(x)

ƒ(x) = cos(x)

ƒ’(x) = -sin(x)

ƒ(x) = tan(x)

ƒ’(x) = sec²(x)

ƒ(x) = cot(x)

ƒ’(x) = -csc²(x)

ƒ(x) = sec(x)

ƒ’(x) = sec(x) × tan(x)

ƒ(x) = csc(x)

ƒ’(x) = -csc(x) × cot(x)

ƒ(x) = sin⁻¹(x); ƒ(x) = arcsin(x)

ƒ’(x) = 1/√(1-x²)

ƒ(x) = cos⁻¹(x); ƒ(x) = arccos(x)

ƒ’(x) = -1/√(1-x²)

ƒ(x) = tan⁻¹(x); ƒ(x) = arctan(x)

ƒ’(x) = 1/(1+x²)

ƒ(x) = cot⁻¹(x); ƒ(x) = arccot(x)

ƒ’(x) = -1/(1+x²)

ƒ(x) = sec⁻¹(x); ƒ(x) = arcsec(x)

ƒ’(x) = 1/(|x|√(x²-1))

ƒ(x) = csc⁻¹(x); ƒ(x) = arccsc(x)

ƒ’(x) = -1/(|x|√(x²-1))

ƒ(x) = ∫sin(x)dx

ƒ(x) = -cos(x) + c

ƒ(x) = ∫cos(x)dx

ƒ(x) = sin(x) + c

ƒ(x) = ∫tan(x)dx

ƒ(x) = -ln|cos(x)| + c

ƒ(x) = ∫cot(x)dx

ƒ(x) = ln|sin(x)| + c

ƒ(x) = ∫csc(x)dx

ƒ(x) = -ln|csc(x) + cot(x)| + c

ƒ(x) = ∫sec(x)dx

ƒ(x) = ln|sec(x) + tan(x)| + c