Reference Angle
See how to find the reference angle of the given angle.
4 examples and their solutions.
Reference Angle
Definition
formed by the x-axis and the terminal side.
It is used to find the trigonometric function values.
Formula
| θ | Reference 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 0 ≤ π4 ≤ π2
π4 → π4
π4 → π4
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Example
Reference angle of 2π3?
Solution π2 ≤ 2π3 ≤ π
2π3 → π - 2π3
= 3π3 - 2π3
= π3
2π3 → π - 2π3
= 3π3 - 2π3
= π3
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Example
Reference angle of 5π4?
Solution π ≤ 5π4 ≤ 3π2 (= 6π4)
5π4 → 5π4 - π
= 5π4 - 4π4
= π4
5π4 → 5π4 - π
= 5π4 - 4π4
= π4
Close
Example
Reference angle of 11π6?
Solution 3π2 ≤ 11π6 ≤ 2π (= 12π6)
11π6 → 2π - 11π6
= 12π6 - 11π6
= π6
11π6 → 2π - 11π6
= 12π6 - 11π6
= π6
Close