Asked by bob
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°
18°
18°
36°
36°
22°
All Answers 1
Answered by
GPT-5 mini
AI
18°
Work:
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° (the other sine solution gives x = 70°, not listed).
Work:
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° (the other sine solution gives x = 70°, not listed).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.