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Math Help - Unit Circle Trig

  1. #1
    Member realintegerz's Avatar
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    Unit Circle Trig

    I need a little helping hand on these 2 problems

    1. Without using a calculator, find all solutions for t for 1 - 2 sin^2 t = 0 where t is in between or equal to 0 and 2pi

    *So I got that sin t was equal to 1 / sq. root 2, but I'm not seeing how it matches up to one of the values of the unit circle...

    2. Suppose alpha and beta are central angles in the unit circle (of radius 1) with initial sides on the positive x-axis. Further suppose that alpha is in quadrant 1 and beta is in quadrant 4 such that sine of alpha is 2/3 and cosine of beta is 1/4

    a) Find the exact value of cosine alpha
    b) Find the exact value of sine beta

    *I have no clue on how to solve these....
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Quote Originally Posted by realintegerz View Post
    I need a little helping hand on these 2 problems

    1. Without using a calculator, find all solutions for t for 1 - 2 sin^2 t = 0 where t is in between or equal to 0 and 2pi

    *So I got that sin t was equal to 1 / sq. root 2, but I'm not seeing how it matches up to one of the values of the unit circle...
    \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}

    look familiar now?

    2. Suppose alpha and beta are central angles in the unit circle (of radius 1) with initial sides on the positive x-axis. Further suppose that alpha is in quadrant 1 and beta is in quadrant 4 such that sine of alpha is 2/3 and cosine of beta is 1/4

    a) Find the exact value of cosine alpha
    b) Find the exact value of sine beta
    from the unit circle, it should be clear to you that for any angle \theta,
    \sin^2{\theta} + \cos^2{\theta} = 1


    \cos{\alpha} = \sqrt{1 - \sin^2{\alpha}}

    \sin{\beta} = -\sqrt{1 - \cos^2{\beta}}
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