PSAT Math Multiple-Choice Question 86: Answer and Explanation

Question: 86

If sin a^o = x, then cos b^o =

• A. x
• B. 1 - x
• C.
• D. x - 1

Correct Answer: A

Explanation:

A

The question asks for the value of a trigonometric function. There are variables in the answer choices, so plug in. You are given a right triangle, so plug in for the sides of the triangle. Use the Pythagorean triple 3-4-5 to make the math easy. Add these side lengths to the figure as follows:

, so calculate sin a° = . Let x = . , so calculate cos b° = . This is the target value; circle it. Now plug x = into the answer choices to see which one matches the target value. Choice (A) becomes . Keep (A), but check (B), (C), and (D) just in case. Choice (B) becomes . This does not match the target, so eliminate (B). Choice (C) becomes . Eliminate (C). Choice (D) becomes . Eliminate (D). The correct answer is (A).