The point (7, 24) is on the terminal side of an angle in standard position.Determine the exact value of cos $\theta$.
A) $\cot \theta = - \frac { 24 } { 7 }$
B) $\cot \theta = \frac { 24 } { 25 }$
C) $\cot \theta = \frac { 25 } { 24 }$
D) $\cot \theta = - \frac { 24 } { 25 }$
E) $\cot \theta = - \frac { 7 } { 24 }$

Question

Quizplus · Accepted Answer

The cosine of an angle is the adjacent side over the hypotenuse. Here, the adjacent side is 7, and the hypotenuse is $\sqrt{7^2 + 24^2} = 25$. Thus, $\cos \theta = \frac{7}{25}$. However, the question asks for $\cot \theta$, which is $\frac{\text{adjacent}}{\text{opposite}} = \frac{7}{24}$, but since the point is in the first quadrant, $\cot \theta$ is positive. Therefore, none of the options directly match $\cos \theta$, but E is the correct expression for $\cot \theta$ if it were negative.

The Point (7, 24) Is on the Terminal Side of an Angle