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Math Help - Simplify the following?

  1. #1
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    Simplify the following?

    How would you simplify

    sin (2 pi + x)

    and sin (-x)

    thank you!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by finalfantasy View Post
    How would you simplify

    sin (2 pi + x)
    use the addition formula for sine

    \sin (A + B) = \sin A \cos B + \sin B \cos A


    and sin (-x)
    sine is an odd function, thus:

    \sin (-x) = - \sin x
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  3. #3
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    Thanks, would those be the answers using the unit circle?
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  4. #4
    Super Member angel.white's Avatar
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    Also, a circle has 2\pi radians in it, so any angle + 2\pi equals that angle.

    It's the same as adding 360 degrees, if you do a 360 you are right back where you started, angle x radians + 2\pi radians = x radians

    you can see this by choosing any x value you like, then typing into a calculator sin(x) and sin(2\pi + x) (make sure your calculator is in radians and not in degrees)

    some suggested values of x that you should try are \frac{\pi}{6}, \frac{5}{6}, \pi
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by finalfantasy View Post
    Thanks, would those be the answers using the unit circle?
    i think the identity is proven using the unit circle but i just know it as the addition formula. but also, angel.white is correct, when we are talking about angles in the unit circle, we obtain equivalent angles by adding 2 \pi to the angle, since we just make one complete revolution and come back to where we started.

    so \sin x = \sin (x + 2n \pi) for n an integer
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