Question

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

a. θ = 30°
b. θ = 45°
c. No such angle exists.
d. θ = 60°

Answer 1

The angle θ in the given equation sin θ = cos θ in the interval [0°, 90°) is equal to 45°.

Step-by-step explanation:

The given equation is sin θ = cos θ. In the interval [0°, 90°), the values of sin θ and cos θ correspond to the values of the sides of a right triangle. Since sin θ represents the length of the side opposite θ and cos θ represents the length of the adjacent side, the equation sin θ = cos θ can be rewritten as the ratio of the opposite side to the adjacent side. That is, sin θ / cos θ, which simplifies to tan θ.

So, tan θ = 1. We know that tan 45° = 1, which means θ = 45° is a solution. Therefore, the answer is (b) θ = 45°