Question

Given the expression sin(3x+10°)=cos(2x−10°)
, which of the following uses the relationship between the sine and cosine of complementary angles to correctly determine the value of x?(1 point)
Responses

36°
36°

16°
16°

18°
18°

22°

Answer 1

Rewrite cos as a sine of the complementary angle:
cos(2x−10°) = sin(90° − (2x−10°)) = sin(100° − 2x).

So sin(3x+10°) = sin(100° − 2x). Thus
3x+10° = 100° − 2x (or the supplementary case gives x = 70°, not in the choices).

Solving 3x+10° = 100° − 2x gives 5x = 90° ⇒ x = 18°.

Answer: 18°.