Question

The sine and cosine of an acute angle are equal. What is the value of angle?
1)30°
2)45°
3)60°
4)Sine and Cosine will never be equal.

1. huyenthanh
The sine and the cosine of the acute angle are the same for θ = π / 4. (Correct choice: 2)

### To what angles both the sine and the cosine have the same value?

Acute angles are angles whose measures are greater than 0° and less than 90°. According to the statement, we must find at least a value such that sin θ = cos θ:
sin θ = cos θ                     Given
sin θ / cos θ = 1                 Compatibility with multiplication / Existence of multiplicative inverse / Modulative property
tan θ = 1                            Definition of tangent
θ = π / 4                            Inverse trigonometric function / Result
In a nutshell, the sine and the cosine of the acute angle are the same for θ = π / 4. (Correct choice: 2)