Right Triangle Relationships and Trigonometry — Test
Question 18 • Geometry
Three trigonometric functions for a given angle are shown. cosecant theta is equal to 13 over 12 , secant theta is equal to negative 13 fifths , cotangent theta is equal to negative 5 over 12 What are the coordinates of point open paren x comma y close paren on the terminal ray of angle theta , assuming that the values above were not simplified?
Answer
A
open paren negative 5 comma 12 close paren
B
open paren 12 comma negative 5 close paren
C
open paren negative 12 comma 5 close paren
D
open paren 5 comma negative 12 close paren
Explanation
Since cosecant θ = 13/12, sine θ = 12/13, so y/r = 12/13. Since secant θ = −13/5, cosine θ = −5/13, so x/r = −5/13. These ratios give the terminal-ray coordinates (x, y) = (−5, 12), which is choice A; the cotangent value also checks out because x/y = −5/12.
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