Ximpledu

Coterminal Angles

See how to find the coterminal angles of the given angle.
5 examples and their solutions.

Coterminal Angles

Definition


θ(360 + θ)°(360⋅2 + θ)°
Coterminal angles are the angles
that have the same terminal side (↗).

Formula

360n + θ (°)
2nπ + θ (rad)
To find the coterminal angles,
add or subtract the multiples of 360° (2π).
360, 720, 1080, ...
2π, 4π, 6π, ...
Radian

Example

Three coterminal angles of 60°
Solution

Example

Three coterminal angles of π4
Solution

Example

θ: coterminal angle of 1000°
θ = ?
(0 ≤ θ ≤ 360°)
Solution

Example

θ: coterminal angle of -1000°
θ = ?
(0 ≤ θ ≤ 360°)
Solution

Example

θ: coterminal angle of 13π2
θ = ?
(0 ≤ θ ≤ 2π)
Solution