Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined."
-$\mathrm { P } ( - 2,5 ) ;$ find $\sin \theta$
A) $- \frac { 5 } { 2 }$
B) $\frac { 2 \sqrt { 29 } } { 29 }$
C) $\frac { 5 \sqrt { 29 } } { 29 }$
D) $\frac { \sqrt { 29 } } { 5 }$

Question

Quizplus · Accepted Answer

The sine of an angle θ, given a point P(-2,5) on its terminal side, is the ratio of the y-coordinate to the hypotenuse of the right triangle formed with the origin. The hypotenuse is $\sqrt{(-2)^2 + 5^2} = \sqrt{4 + 25} = \sqrt{29}$, so $\sin \theta = \frac{5}{\sqrt{29}} = \frac{5\sqrt{29}}{29}$.

Point P Is on the Terminal Side of θ P(−2,5);\mathrm { P } ( - 2,5 ) ;P(−2,5);

Point P Is on the Terminal Side of θ $\mathrm { P } ( - 2,5 ) ;$