The terminal side of $\theta$ lies on the given line in the specified quadrant. Find the value of the given trigonometric function of $\theta$ by finding a point on the line.
$\begin{array} { c c l } \text { Line } & \text { Quadrant } & \text { Evaluate: } \ y = 10 x & \text { I } & \cos \theta \end{array}$

A) $\sqrt { 101 }$

B) $\frac { 1 } { \sqrt { 101 } }$

C) $\frac { 1 } { 10 }$

D) $\frac { 10 } { \sqrt { 101 } }$
E) $- \frac { 10 } { \sqrt { 101 } }$

Question

The terminal side of $\theta$ lies on the given line in the specified quadrant. Find the value of the given trigonometric function of $\theta$ by finding a point on the line.
$\begin{array} { c c l } \text { Line } & \text { Quadrant } & \text { Evaluate: } \ y = 10 x & \text { I } & \cos \theta \end{array}$

A) $\sqrt { 101 }$

B) $\frac { 1 } { \sqrt { 101 } }$

C) $\frac { 1 } { 10 }$

D) $\frac { 10 } { \sqrt { 101 } }$
E) $- \frac { 10 } { \sqrt { 101 } }$

Quizplus · Accepted Answer

In the first quadrant, both x and y are positive. A point on the line $y = 10x$ can be $(1, 10)$. The hypotenuse is $\sqrt{1^2 + 10^2} = \sqrt{101}$. Thus, $\cos \theta = \frac{x}{\text{hypotenuse}} = \frac{1}{\sqrt{101}}$.

The Terminal Side Of θ\thetaθ Lies on the Given Line in the Specified Quadrant

The Terminal Side Of $\theta$ Lies on the Given Line in the Specified Quadrant