Geometry and TrigonometryHardSine and cosine of complementary angles
Geometry and Trigonometry practice question
If sin 35° = cos x°, and 0 < x < 90, what is the value of x?
- A. 55Correct
- B. 35
- C. 145
- D. 65
Answer: A. 55
For acute angles, the sine of an angle equals the cosine of its complement: sin θ = cos(90° − θ). So sin 35° = cos 55°, and x = 55.
Why the other answers are wrong
- B. 35
- sin 35° and cos 35° are different numbers (about 0.574 and 0.819). The angle whose cosine equals sin 35° is 90° − 35°.
- C. 145
- 145 is 180° − 35°, the supplement. Sine and cosine swap for COMPLEMENTARY angles, which add to 90°.
- D. 65
- 65 is 100 − 35. The complement is found by subtracting from 90, giving 55.
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