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°

18°
18°

16°
16°

22°
22°

Answer 1

Use sin A = cos B = sin(90° − B). So
3x + 10° = 90° − (2x − 10°) + 360k
3x + 10° = 100° − 2x + 360k
5x = 90° + 360k
x = 18° + 72k.

Taking k = 0 (principal solution) gives x = 18°.