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Math Help - Please help with solving trig equations!

  1. #1
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    Please help with solving trig equations!




    THANKS!
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by gobbajeezalus View Post



    THANKS!
    (1) \sin x \tan x - \sin x=0

    \sin x(\tan x-1)=0

    \sin x = 0 \ \ or \ \ \tan x-1=0

    \tan x=1

    \sin x=0 \ \ at \ \ \left\{0, \pi \right\}

    \tan x=1 \ \ at \ \ \left\{\frac{\pi}{4}, \frac{5\pi}{4}\right\}

    Solution set= \left\{0, \frac{\pi}{4}, \pi, \frac{5\pi}{4}\right\}
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  3. #3
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    Quote Originally Posted by gobbajeezalus View Post



    THANKS!
    (2) \sin 2x=-\sin x

    \sin 2x+\sin x

    Double angle identity: \sin 2x = 2\sin x \cos x

    2\sin x \cos x + \sin x=0

    \sin x(2\cos x+1)=0

    \boxed{\sin x = 0} \ \ or \ \ 2\cos x+1=0

    2\cos x=-1

    \boxed{\cos x = -\frac{1}{2}}

    \sin x=0 \ \ at \ \ \left\{0, \pi\right\}

    \cos x = -\frac{1}{2} \ \ at \ \ \left\{\frac{2\pi}{3}, \frac{4\pi}{3}\right\}

    Solution set= \left\{0, \pi, \frac{2\pi}{3}, \frac{4\pi}{3}\right\}
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  4. #4
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    Quote Originally Posted by gobbajeezalus View Post



    THANKS!
    (3) 2\sin \theta \cos \theta + \sqrt{3} \sin \theta = 0

    \sin \theta(2 \cos \theta + \sqrt{3})=0

    \boxed{\sin \theta=0} \ \ or \ \ 2 \cos \theta = -\sqrt{3}

    \boxed{\cos \theta = -\frac{\sqrt{3}}{2}}

    \sin \theta = 0 \ \ at \ \ \left\{0, \pi\right\}

    \cos \theta = -\frac{\sqrt{3}}{2} \ \ at \ \ \left\{\frac{5\pi}{6}, \frac{7\pi}{6}\right\}

    Solution set= \left\{0, \frac{5\pi}{6}, \pi, \frac{7\pi}{6}\right\}
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