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Math Help - Trigonometric Function: Find Terminal side of Angle θ

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    Trigonometric Function: Find Terminal side of Angle θ

    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.
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    Re: Trigonometric Function: Find Terminal side of Angle θ

    Quote Originally Posted by RCurtis View Post
    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.
    \sin \theta =\frac{12}{\sqrt{12^2+9^2}}=\frac{4}{5}
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    Re: Trigonometric Function: Find Terminal side of Angle θ

    Quote Originally Posted by princeps View Post
    \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?
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    Re: Trigonometric Function: Find Terminal side of Angle θ

    Quote Originally Posted by RCurtis View Post
    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...
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    Re: Trigonometric Function: Find Terminal side of Angle θ

    Quote Originally Posted by RCurtis View Post
    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. 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:

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

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