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Math Help - How to find the critical angle

  1. #1
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    How to find the critical angle

    How would I find the critical angle of
    V'(t)=22500*(cos(t)^2)-(100*(225+225*sin(t)))*sin(t)


    (just to let you know, t us used in place of )

    thanks!
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by Theressa View Post
    How would I find the critical angle of
    V'(t)=22500*(cos(t)^2)-(100*(225+225*sin(t)))*sin(t)


    (just to let you know, t us used in place of )

    thanks!
    22500\cos^2(t)-(22500+22500\sin(t))\sin(t)= 22500(1-\sin^2(t))-22500\sin^2(t))-22500\sin(t) =22500-22500\sin^2(t)-22500\sin^2(t)-22500\sin(t) =22500(1-\sin(t)-2\sin^2(t))=22500(1-2\sin(t))(1+\sin(t))

    Solve 22500(1-2\sin(t))(1+\sin(t))=0 for t to get t=\left\{\frac{\pi}{6},\frac{5\pi}{6},\frac{3\pi}{  2}\right\}
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