Thread: 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.

Originally Posted by RCurtis

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.

Originally Posted by princeps

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

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...

Originally Posted by RCurtis

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.

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. . 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: