Geometry and TrigonometryVery hardRelationship between sine and cosine of complementary angles
Geometry and Trigonometry practice question
In right triangle PQR, angle R is the right angle and sin P = 0.6. What is cos Q?
- A. 0.6Correct
- B. 0.8
- C. 0.4
- D. 1.2
Answer: A. 0.6
Angles P and Q are complementary (P + Q = 90°), and the sine of an angle equals the cosine of its complement: cos Q = sin P = 0.6.
Why the other answers are wrong
- B. 0.8
- 0.8 is cos P (or sin Q), the other ratio.
- C. 0.4
- 0.4 is 1 − 0.6; sine and cosine of complements are equal, not complements of each other.
- D. 1.2
- 1.2 is not possible for a cosine (at most 1).
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