Trigonometric Function: Find Terminal side of Angle θ

• Apr 3rd 2012, 07:03 AM
RCurtis
Trigonometric 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 AM
princeps
Re: Trigonometric Function: Find Terminal side of Angle θ
Quote:

Originally Posted by RCurtis
Stuck here, any takers?
---

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.

$\displaystyle \sin \theta =\frac{12}{\sqrt{12^2+9^2}}=\frac{4}{5}$
• Apr 3rd 2012, 07:26 AM
RCurtis
Re: Trigonometric Function: Find Terminal side of Angle θ
Quote:

Originally Posted by princeps
$\displaystyle \sin \theta =\frac{12}{\sqrt{12^2+9^2}}=\frac{4}{5}$

Awesome, other than the obvious arithmetic, how did you arrive at this particular setup to get the answer?
• Apr 3rd 2012, 08:18 AM
princeps
Re: Trigonometric Function: Find Terminal side of Angle θ
Quote:

Originally Posted by RCurtis
Awesome, other than the obvious arithmetic, how did you arrive at this particular setup to get the answer?

If you make a drawing you will see that solution is almost obvious...
• Apr 3rd 2012, 11:29 AM
masters
Re: Trigonometric Function: Find Terminal side of Angle θ
Quote:

Originally Posted by RCurtis
Stuck here, any takers?
---

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.

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:

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