Ximpledu

Trigonometric Equation

See how to solve a trigonometric equation
(sine/cosine/tangent equation).
3 examples and their solutions.

Sine Equation

Formula

sin x = k
→ x = nπ + (-1)nθ
How to find:
1. Find one root of the equation: x = θ.
2. Put this into x = nπ + (-1)nθ.

Example

sin x = 12
(0 ≤ x ≤ 2π)
Solution

Cosine Equation

Formula

cos x = k
→ x = 2nπ ± θ
How to find:
1. Find one root of the equation: x = θ.
2. Put this into x = 2nπ ± θ.

Example

cos x = -22
(0 ≤ x ≤ 2π)
Solution

Tangent Equation

Formula

tan x = k
→ x = nπ + θ
How to find:
1. Find one root of the equation: x = θ.
2. Put this into x = nπ + θ.

Example

tan x = √3
(0 ≤ x ≤ 2π)
Solution