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Math Help - Trignometry

  1. #1
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    Trignometry

    1) Simpifly
    sin^2 (sin^-1 (4/x))


    2) a,b (0,2pi)and sin (a)=sqrt(3)/2, cos(b)=-sqrt(3)/2, tan(a+b)=-1/sqrt(3), then give the exact value of a and b in terms of pi

    a: ____pi b:_____pi
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  2. #2
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    Quote Originally Posted by lemontea View Post
    2) a,b (0,2pi)and sin (a)=sqrt(3)/2, cos(b)=-sqrt(3)/2, tan(a+b)=-1/sqrt(3), then give the exact value of a and b in terms of pi

    a: ____pi b:_____pi
    There are two angles such that \sin(a)=\frac{\sqrt{3}}{2} \\\ a=\frac{\pi}{3}\mbox{ or }\frac{2\pi}{3}

    Also with cosine \cos(b)=-\frac{3}{2} \\\ b=\frac{5\pi}{6} \mbox{ or } \frac{7\pi}{6}

    and \tan(a+b)=-\frac{1}{\sqrt{3}} \\\ a+b=\frac{5\pi}{6} \mbox{ or } \frac{11\pi}{6}

    So for this to be true a=\frac{2\pi}{3} \\\ b=\frac{7\pi}{6} \\\ a+b=\frac{11\pi}{6}

    Hint: for the first one \sin^2\left( \sin^{-1}\left( \frac{4}{x}\right)\right)= \left[\sin\left(\sin^{-1}\left( \frac{4}{x}\right)\right)\right]^2
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