Find the angle θ (if it exists) in the interval [0°, 90°) for which sin θ = cos θ?

Solution:

We know that in a triangle

sin θ = opposite/ hypotenuse

cos θ = adjacent/ hypotenuse

In a right angled triangle, where both opposite and adjacent sides are equal 

sin θ = cos θ

It would be an isosceles right triangle, where the angles are 45°, 45° and 90°.

sin (45°) = 0.70711

cos (45°) = 0.70711

Therefore, the angle θ is 45°.

Find the angle θ (if it exists) in the interval [0°, 90°) for which sin θ = cos θ?

Summary:

The angle θ (if it exists) in the interval [0°, 90°) for which sin θ = cos θ is 45°.