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°

36°
36°

18°
18°

22°
22°

Answer 1

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

3x + 10° = 100° − 2x => 5x = 90° => x = 18°
(or 3x + 10° = 180° − (100° − 2x) gives x = 70°, not listed)

Answer: 18°.