Question

If 0 ≤ x ≤ 90°, state the numerical value of x for which sin x° = cos x°.

Answer 1

Given: sin x° = cos x°, where 0° ≤ x ≤ 90°.

Step-wise calculation:

1. Check endpoint x = 90°:

cos 90° = 0 while sin 90° = 1

So, x = 90° is not a solution.

2. For 0° ≤ x < 90° we may divide both sides by cos x (cos x ≠ 0): tan x = 1.

3. Solve tan x = 1

⇒ x = arctan(1)

= 45°

Equivalently, sin x = cos x implies sin x = sin (90° – x).

So, x = 90° – x

⇒ 2x = 90°

⇒ x = 45°