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°

16°
16°

36°
36°

18°

Answer 1

18°

Work: sin(3x+10°) = cos(2x−10°) = sin(90° − (2x−10°)) = sin(100° − 2x).
So 3x + 10° = 100° − 2x ⇒ 5x = 90° ⇒ x = 18°.