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A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ.
-$\left( - \frac { 1 } { 5 } , \frac { 1 } { 3 } \right)$
Find $\cos \theta$.
A) $- \frac { 34 } { 5 }$
B) $\frac { 5 \sqrt { 34 } } { 34 }$
C) $- \frac { 3 \sqrt { 34 } } { 34 }$
D) $\frac { 34 } { 3 }$

Question

Quizplus · Accepted Answer

The cosine of an angle is the x-coordinate divided by the hypotenuse. The hypotenuse is $\sqrt{\left(-\frac{1}{5}\right)^2 + \left(\frac{1}{3}\right)^2} = \sqrt{\frac{1}{25} + \frac{1}{9}} = \sqrt{\frac{34}{225}}$. Thus, $\cos \theta = \frac{-\frac{1}{5}}{\sqrt{\frac{34}{225}}} = -\frac{3\sqrt{34}}{34}$.

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