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Thread: How do I use reference angles to find these answers?

  1. #1
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    How do I use reference angles to find these answers?

    The problem says use reference angle method and gives me this:

    1.) tanx = sq root of 3, 0< x < 4pie

    2.) 2sin^2(x) + cosx = 1, 0< x< 2pie

    I mean, I understand enough of sine and cosine to understand what it's asking, but I don't know exactly the proper steps to find the answer. Any help would be greatly appreciated.
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    Quote Originally Posted by I_needhelp View Post
    The problem says use reference angle method and gives me this:

    1.) tanx = sq root of 3, 0< x < 4pie

    2.) 2sin^2(x) + cosx = 1, 0< x< 2pie

    I mean, I understand enough of sine and cosine to understand what it's asking, but I don't know exactly the proper steps to find the answer. Any help would be greatly appreciated.
    1. $\displaystyle \tan{x} = \sqrt{3}, 0 < x < 4\pi$


    $\displaystyle x = \tan^{-1}{\sqrt{3}}$

    There will be an answer in the first quadrant, and an answer in the third.

    So $\displaystyle x = \{\frac{\pi}{3},\pi + \frac{\pi}{3}\}$.

    Also, every iteration of the unit circle will have 2 solutions. This can be represented by adding $\displaystyle 2n\pi$, where $\displaystyle n$ is an integer.

    So $\displaystyle x = \{\frac{\pi}{3}, \frac{4\pi}{3}\} + 2n\pi$.

    Letting n equal different values enables you to find all solutions in the domain.

    Let $\displaystyle n = 0$ you have $\displaystyle x = \{\frac{\pi}{3}, \frac{4\pi}{3}\}$

    Let $\displaystyle n = 1$, you have $\displaystyle x = \{\frac{7\pi}{3}, \frac{10\pi}{3}\}$.

    Any $\displaystyle n > 1$ has solutions out of the domain.

    So all the solutions are

    $\displaystyle x=\{\frac{\pi}{3}, \frac{4\pi}{3}, \frac{7\pi}{3}, \frac{10\pi}{3}\}$.
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