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°

36°
36°

16°
16°

22°
22°

Answer 1

18°

Reason: sin(3x+10°)=cos(2x−10°) implies 3x+10° = 90° − (2x−10°) + 360k or 3x+10° = 90° + (2x−10°) + 360k. The first gives 3x+10 = 100 − 2x + 360k → 5x = 90 + 360k → x = 18° + 72k. Taking k = 0 yields x = 18°, which is the choice listed. (The other case gives x = 70° + 360k.)