MCAT Math Question 9: Answer and Explanation
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Question: 9
9. Which of the following relationships is INCORRECT?
- A. |sin θ × cos θ| < |sin θ| + |cos θ|
- B. sin θ ÷ cos θ = tan θ
- C. tan 90° is undefined
- D. sin θ = sin (90° - θ)
Correct Answer: D
Explanation:
sin θ ≠ sin (90° ? θ), although sin θ = cos (90° ? θ). The other statements must all be true. Because sine and cosine values are always between ?1 and 1, the product of sine and cosine will always have a magnitude less than 1. The sum of the absolute value of sine and the absolute value of cosine, on the other hand, will always be greater than 1. Therefore, choice (A) can be eliminated. Because sine is the ratio of opposite to hypotenuse and cosine is the ratio of adjacent to hypotenuse, the quotient between the two is the ratio of opposite to adjacent, or the tangent of the angle. Therefore, choice (B) can be eliminated. By the same logic, because sin 90° = 1 and cos 90° = 0, tan 90° is undefined, eliminating choice (C).