Ximpledu

Reference Angle

See how to find the reference angle of the given angle.
4 examples and their solutions.

Reference Angle

Definition

A reference angle is the smaller angle
formed by the x-axis and the terminal side.
It is used to find the trigonometric function values.

Formula

θReference Angle
0 ≤ θ ≤ π2 θ → θ
π2 ≤ θ ≤ π θ → π - θ
π ≤ θ ≤ 3π2 θ → θ - π
3π2 ≤ θ ≤ 2π θ → 2θ - π

Example

Reference angle of π4?
Solution

Example

Reference angle of 2π3?
Solution

Example

Reference angle of 5π4?
Solution

Example

Reference angle of 11π6?
Solution