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Math Help - Sine and Cosine

  1. #1
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    Sine and Cosine

    My professor taught us to solve few questions of sine by doing this. I don't understand what he did to get the answer. I can get the answer without doing any steps but I need to understand how he has done it.

    Question:

    sin(11pi/2)
    = sin (3pi/2 + 8pi/2)
    = sin (3pi/2 + 4pi)
    = sin (3pi/2) <--- i don't know why 4pi just disappears.
    = -1

    Can I also get a different example with cosine and a negative sign so I can understand better. Thanks.
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  2. #2
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    Re: Sine and Cosine

    Quote Originally Posted by qwerty999 View Post
    My professor taught us to solve few questions of sine by doing this. I don't understand what he did to get the answer. I can get the answer without doing any steps but I need to understand how he has done it.

    Question:

    sin(11pi/2)
    = sin (3pi/2 + 8pi/2)
    = sin (3pi/2 + 4pi)
    = sin (3pi/2) <--- i don't know why 4pi just disappears.
    = -1

    Can I also get a different example with cosine and a negative sign so I can understand better. Thanks.
    Using a diagram of the Unit Circle, centre (0,0) and radius equal to 1 unit,
    the vertical co-ordinate of a point on the circumference is the Sine of the angle.

    When the angle is zero, the vertical co-ordinate is zero.
    When the angle is 90 degrees, the vertical co-ordinate is 1.
    When the angle is 180 degrees, the vertical co-ordinate is 0.
    When the angle is 270 degrees, the vertical co-ordinate is -1.

    Another 90 degrees on and we are back where we started.
    Hence any multiple of 360 degrees added to the angle gives us the same vertical co-ordinate.
    Knowing the periodicity allows you to determine the Sine of your given angle
    by subtracting 360 degrees twice.
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  3. #3
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    Re: Sine and Cosine

    Quote Originally Posted by qwerty999 View Post
    My professor taught us to solve few questions of sine by doing this. I don't understand what he did to get the answer. I can get the answer without doing any steps but I need to understand how he has done it.

    Question:

    sin(11pi/2)
    = sin (3pi/2 + 8pi/2)
    = sin (3pi/2 + 4pi)
    = sin (3pi/2) <--- i don't know why 4pi just disappears.
    = -1

    Can I also get a different example with cosine and a negative sign so I can understand better. Thanks.
    It's because the angle \displaystyle \frac{3\pi}{2} + 4\pi is in the same position as the angle \displaystyle \frac{3\pi}{2}, you've just moved around the unit circle twice before getting to it. That means their sines are equal.
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