In triangle RST above, point W (not shown) lies on RT. What is the value of cos(∠RSW ) − sin(∠WST )?
Correct answer: A. 0
- A. 0
- B. 1
- C. 2
- D. 3
Explanation
The correct answer is 0. Note that no matter where point W is on _ RT, the sum of the measures of ∠RSW and ∠WST is equal to the measure of ∠RST, which is 90°. Thus, ∠RSW and ∠WST are complementary angles. Since the cosine of an angle is equal to the sine of its complementary angle, cos(∠RSW) = sin(∠WST). Therefore, cos(∠RSW) − sin(∠WST) = 0.
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