SAT Math Multiple Choice Question 342: Answer and Explanation

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Question: 342

12. The value of cos 40° is the same as which of the following?

  • A. sin 50°
  • B. sin(–40°)
  • C. cos(–50°)
  • D. cos 140°

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Additional Topics in Math / Trigonometry

Strategic Advice: The measure of 40° does not appear on the unit circle, which should give you a clue that there must be a property or relationship on which you can rely to help you answer the question.

Getting to the Answer: Complementary angles have a special relationship relative to trig values: The cosine of an acute angle is equal to the sine of the angle's complement and vice versa. Because only one of the answers can be correct, look for the simplest relationship (complementary angles): 50° is complementary to 40°, so cos 40° = sin 50°, which means (A) is correct.

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