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

18°
18°

16°
16°

22°
22°

36°
36°

Answer 1

Use sin θ = cos(90° − θ). So
sin(3x + 10°) = cos(2x − 10°) = sin(90° − (2x − 10°)) = sin(100° − 2x).

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

(Other periodic solutions exist, but among the choices the correct value is 18°.)