객관식
Given a right triangle where one of the acute angles is , and the side opposite has length , the side adjacent to has length , and the hypotenuse has length , what are the exact values of the six trigonometric ratios for angle ?
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2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
Multiple Choice
In a right triangle, for angle , what is the trigonometric ratio for ?
A
B
C
D
검증된 단계별 안내1
Recall the definition of the sine function in a right triangle: for an angle \( C \), \( \sin(C) \) is the ratio of the length of the side opposite angle \( C \) to the length of the hypotenuse.
Identify the sides of the triangle relative to angle \( C \): the 'opposite' side is the one directly across from angle \( C \), the 'adjacent' side is next to angle \( C \) but not the hypotenuse, and the 'hypotenuse' is the longest side opposite the right angle.
Write the sine ratio using these side names: \( \sin(C) = \frac{\text{opposite}}{\text{hypotenuse}} \).
Compare this ratio to the given options to determine which one correctly represents \( \sin(C) \).
Remember that \( \sin(C) \) is never the ratio of opposite to adjacent, adjacent to hypotenuse, or hypotenuse to opposite; it must always be opposite over hypotenuse.
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