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Math Help - Trigonometry question

  1. #1
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    Trigonometry question

    [SIZE=4]If A=sin(-1)x, where x>0 sin(-1)x means the shift sin in the calulator of angle x
    Two part question
    a)show that cosA=squareroot of 1-x^2


    b)find expressions in terms of x for cosecA and cos2A[/SIZE
    ]
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by kingkaisai2
    [SIZE=4]If A=sin(-1)x, where x>0 sin(-1)x means the shift sin in the calulator of angle x
    [SIZE=5]Two part question
    a)show that cosA=squareroot of 1-x^2

    If:

    A=\arcsin(x)

    then:

    <br />
x=\sin (A)<br />

    but:

    (\sin(A))^2+(\cos(A))^2=1,

    so:

    x^2+(\cos(A))^2=1.

    Rearranging gives:

    <br />
\cos(A)=\pm \sqrt{1-x^2}<br />

    Now as x>0, A\in (0,\pi), and so \cos(A)>0, so we
    want the positive square root in the last equation so:

    <br />
\cos(A)= \sqrt{1-x^2}<br />

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by kingkaisai2
    [SIZE=4]If A=sin(-1)x, where x>0 sin(-1)x means the shift sin in the calulator of angle x


    b)find expressions in terms of x for cosecA and cos2A[/SIZE
    ]
    \csc(A)=1/ \sin(A)=1/x.

    \cos(2A)=2 (cos(A))^2-1=2(1-x^2)-1=1-x^2

    RonL
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