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

16°
16°

22°
22°

18°
18°

36°

Answer 1

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

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

(There is a second family 3x+10 = 90 + (2x−10) giving x = 70°, but the choice matching the first solution is 18°.)