Three trigonometric functions for a given angle are shown below:

Cosecant theta = 13/12; Secant theta = -13/5; Cotangent theta = -5/12.

What are the coordinates of point (x, y) on the terminal ray of angle Theta, assuming that the values above were not simplified?

Options:

(–5, 12)
(5, –12)
(–12, 5)
(12, –5)

To find the coordinates of the point ( x , y ) on the terminal ray of angle θ , we can use the definitions and relations of trigonometric functions.
Given:

csc θ = 12 13 ​

sec θ = − 5 13 ​

cot θ = − 12 5 ​


Let's analyze each function:

Cosecant : csc θ = s i n θ 1 ​


If csc θ = 12 13 ​ , then sin θ = 13 12 ​ .


Secant : sec θ = c o s θ 1 ​


If sec θ = − 5 13 ​ , then cos θ = − 13 5 ​ .


Cotangent : cot θ = t a n θ 1 ​


If cot θ = − 12 5 ​ , then tan θ = − 5 12 ​ .

Now, we need to determine the point ( x , y ) on the terminal side. The basic trigonometric identity for angle θ with hypotenuse r is:

x = r cos θ

y = r sin θ


Since sin θ = 13 12 ​ and cos θ = − 13 5 ​ , it indicates:

y = 12

x = − 5


Thus, the coordinates of point ( x , y ) are ( − 5 , 12 ) .
Therefore, the chosen multiple-choice option is ( − 5 , 12 ) .

Answered by LiamAlexanderSmith | 2025-07-21

The coordinates of the point (x, y) on the terminal ray of angle θ are (-5, 12). This result is derived from the values of the trigonometric functions provided. Therefore, the correct option is A: (-5, 12).
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Answered by LiamAlexanderSmith | 2025-07-22