The terminal side of $\theta$ line $- 15 x - 8 y = 0$ in the fourth quadrant.Find the exact value of $\cos \theta$ .
A) $\cos \theta = \frac { 8 } { 17 }$
B) $\cos \theta = \frac { 8 } { 25 }$
C) $\cos \theta = \frac { 25 } { 52 }$
D) $\cos \theta = \frac { 17 } { 8 }$
E) $\cos \theta = \frac { 25 } { 17 }$

Question

Quizplus · Accepted Answer

The equation of the line can be rewritten as $y = -\frac{15}{8}x$, indicating a slope and a direction. In the fourth quadrant, the cosine of an angle is positive, and it represents the adjacent side over the hypotenuse in a right triangle. By choosing points that fit the line equation and are easy to work with, such as $x = 8$ and $y = -15$, we can form a right triangle with sides 8 (adjacent), 15 (opposite), and 17 (hypotenuse, found using the Pythagorean theorem). Therefore, $\cos \theta = \frac{8}{17}$.

The Terminal Side Of θ\thetaθ Line −15x−8y=0- 15 x - 8 y = 0−15x−8y=0

The Terminal Side Of $\theta$ Line $- 15 x - 8 y = 0$