The point $( - 7 , - 24 )$ is on the terminal side of an angle in standard position.Determine the exact value of $\cos \theta$ .
A) $\cos \theta = \frac { 7 } { 24 }$
B) $\cos \theta = - \frac { 18 } { 7 }$
C) $\cos \theta = - \frac { 7 } { 25 }$
D) $\cos \theta = \frac { 31 } { 7 }$
E) $\cos \theta = \frac { 24 } { 7 }$

Question

Quizplus · Accepted Answer

The cosine of an angle in standard position with a point $(x, y)$ on its terminal side is given by $\cos \theta = \frac{x}{r}$, where $r$ is the distance from the origin to the point, calculated as $\sqrt{x^2 + y^2}$. For the point $(-7, -24)$, $r = \sqrt{(-7)^2 + (-24)^2} = \sqrt{49 + 576} = \sqrt{625} = 25$. Thus, $\cos \theta = \frac{-7}{25} = -\frac{7}{25}$.

The Point (−7,−24)( - 7 , - 24 )(−7,−24) Is on the Terminal Side of an Angle in Standard

The Point $( - 7 , - 24 )$ Is on the Terminal Side of an Angle in Standard