Trigonometry of General Triangles and Trigonometric Functions — Test

Question 14 • Mathematics III

The angle measures associated with which set of ordered pairs share the same reference angle?

Answer

open paren negative the fraction with numerator square root of 3 and denominator 2 comma negative 1 half close paren , open paren negative 1 half comma negative the fraction with numerator square root of 3 and denominator 2 close paren

open paren negative 1 half comma negative the fraction with numerator square root of 3 and denominator 2 close paren , open paren 1 half comma the fraction with numerator square root of 3 and denominator 2 close paren

open paren the fraction with numerator square root of 3 and denominator 2 comma 1 half close paren , open paren 1 half comma the fraction with numerator square root of 3 and denominator 2 close paren

open paren 1 half comma negative the fraction with numerator square root of 3 and denominator 2 close paren , open paren negative the fraction with numerator square root of 3 and denominator 2 comma 1 half close paren

Explanation

For a point on the unit circle, the coordinates are (cos θ, sin θ). In choice D, (−1/2, −√3/2) corresponds to 240°, whose reference angle is 60°. The point (1/2, √3/2) corresponds to 60°, which also has a 60° reference angle, so choice D is correct.

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