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°

22°
22°

16°
16°

36°

Answer 1

Use cos θ = sin(90° − θ):

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

So either
3x + 10° = 100° − 2x ⇒ 5x = 90° ⇒ x = 18°
(or 3x + 10° = 180° − (100° − 2x) ⇒ x = 70°, not in the choices).

Answer: 18°.