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Thread: Trig

  1. #1
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    Trig

    Could someone please show me how to do these step by step please

    a) Find the values of thita in the interval 0<theta<360 for which

    sin(theta)tan(theta)-cos(theta)=1

    b) Find in terms of pie, the values of x in the interval 0<x<2(pie) for which

    3tanx-2cosx=0

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  2. #2
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    Quote Originally Posted by Colin_m View Post
    Could someone please show me how to do these step by step please

    a) Find the values of thita in the interval 0<theta<360 for which

    sin(theta)tan(theta)-cos(theta)=1

    b) Find in terms of pie, the values of x in the interval 0<x<2(pie) for which

    3tanx-2cosx=0

    Because I'm lazy, let $\displaystyle t = \theta$.

    a) $\displaystyle \Rightarrow \frac{\sin^2 t}{\cos t} - \cos t = 1$

    $\displaystyle \Rightarrow \sin^2 t - \cos^2 t = \cos t$

    $\displaystyle \Rightarrow (1 - \cos^2 t) - \cos^2 t = \cos t$

    $\displaystyle \Rightarrow 2 \cos^2 t + \cos t - 1 = 0$


    $\displaystyle \Rightarrow (2 \cos^2 - 1)(\cos t + 1) = 0$.

    All blue sky from here.

    ---------------------------------------------------------------------------

    b) $\displaystyle \Rightarrow \frac{3 \sin x}{\cos x} -2 \cos x=0$

    $\displaystyle \Rightarrow 3 \sin x - 2 \cos^2 x = 0$

    $\displaystyle \Rightarrow 3 \sin x - 2 (1 - \sin^2 x) = 0$

    $\displaystyle \Rightarrow 3 \sin x - 2 + 2 \sin^2 x = 0$

    $\displaystyle \Rightarrow 2 \sin^2 x + 3 \sin x - 2 = 0$

    $\displaystyle \Rightarrow (2 \sin x - 1)(\sin x + 2) = 0$.

    All blue sky from here.
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