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

18°
18°

36°
36°

22°
22°

16°
16°

Answer 1

18°

Reason: cos(2x−10°)=sin(90°−(2x−10°))=sin(100°−2x). So 3x+10°=100°−2x ⇒ 5x=90° ⇒ x=18°. (The other general solution gives x=70°, not listed.)