Question

Given the expression sin(3x+10°)=cos(2x−10°)
sin
⁡
(
3
𝑥
+
10
°
)
=
cos
⁡
(
2
𝑥
−
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

22°
22°

18°
18°

36°
36°

16°

Answer 1

Use sin θ = cos(90° − θ). Rewrite the right side:
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°.

(There is a second family x = 70° + 360k, but from the choices the correct answer is 18°.)