A point on the terminal side of angle θ is given. Find the exact value of the indicated trigonometric function of θ.
-$( 9,12 )$ Find $\cos \theta$.
A) $\frac { 3 } { 5 }$
B) $\frac { 4 } { 5 }$
C) $\frac { 3 } { 4 }$
D) $\frac { 4 } { 3 }$

Question

Quizplus · Accepted Answer

The cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse. Given the point (9,12), we can form a right triangle with legs of lengths 9 and 12. The hypotenuse can be found using the Pythagorean theorem: $\sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15$. Therefore, $\cos \theta = \frac{adjacent}{hypotenuse} = \frac{9}{15} = \frac{3}{5}$.

A Point on the Terminal Side of Angle θ Is (9,12)( 9,12 )(9,12)

A Point on the Terminal Side of Angle θ Is $( 9,12 )$