← Back

Module 6: Trig Equations Quick Ref

Solving Steps

1. Isolate trig function | 2. Find reference angle | 3. All solutions in interval | 4. General solution

General Solutions

sinθ=k → θ=arcsin(k)+2nπ or (π−arcsin(k))+2nπ
cosθ=k → θ=±arccos(k)+2nπ
tanθ=k → θ=arctan(k)+nπ

Inverse Functions

DomainRange
arcsin[−1,1][−π/2, π/2]
arccos[−1,1][0, π]
arctanall reals(−π/2, π/2)

Multiple Angles

sin(nx)=k: solve for u=nx on [0, 2nπ), then x=u/n
NEVER divide by a trig function — FACTOR instead!