Stuck here, any takers?

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A point on the terminal side of angleθ,is given. Find the exact value of the indicated Trigonometric Function ofθ.

(9,12); Find the sinθ.

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- Apr 3rd 2012, 07:03 AMRCurtisTrigonometric Function: Find Terminal side of Angle θ
*Stuck here, any takers?*

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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 the sin**θ.** - Apr 3rd 2012, 07:13 AMprincepsRe: Trigonometric Function: Find Terminal side of Angle θ
- Apr 3rd 2012, 07:26 AMRCurtisRe: Trigonometric Function: Find Terminal side of Angle θ
- Apr 3rd 2012, 08:18 AMprincepsRe: Trigonometric Function: Find Terminal side of Angle θ
- Apr 3rd 2012, 11:29 AMmastersRe: Trigonometric Function: Find Terminal side of Angle θ
To expand a little on what princeps showed you, if you plot the point (9, 12) in the coordinate plane, and drop a perpendicular to the x-axis and a line back to the origin, you will have formed a right triangle. You will note that x = 9 and y = 12.

You need to find r, the length of the hypotenuse. Use the Pythagorean Theorem. $\displaystyle r^2=x^2+y^2$. We determine that r = 15.

Since we know that sin of an acute angle in a right triangle is the ratio of the opposite side of the angle divided by the hypotenuse, we can say:

$\displaystyle \sin \theta = \frac{y}{r}= \frac{12}{15}=\frac{4}{5}$