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6 Answers

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  • 8 months ago

    sin(x)=7/25, 0<x<pi/2

    cos(x-3pi/2)

    =

    cos[-(3pi/2-x)]

    =

    cos(3pi/2-x)

    {note that cos(-x)=cos(x)}

    =

    -sin(x)

    =

    -7/25.

    Alternatively,

    cos(x-3pi/2)

    =

    cos(x)cos(3pi/2)+sin(x)sin(3pi/2)

    =

    0+sin(x)(-1)

    =

    -sin(x)

    =

    -7/25.

  • Como
    Lv 7
    8 months ago

    cos ( x  - 3π/2 )   =  cos x cos 3 π/2  + sin x sin 3 π/2

    cos ( x  - π/2 ) =  - sin x   = -7/25

  • Philip
    Lv 6
    8 months ago

    x is in (0,pi/2). sinx = (7/25). Now cos(x -3pi/2) = cos[(x -3pi/2) +2pi] =

    cos(x +pi/2) = -sinx = -(7/25).

  • alex
    Lv 7
    8 months ago

    cos(x - (3pi/2))=cos(x -(3pi/2)+2pi) = cos(x+(pi/2)) = -sinx = -7/25

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  • Dixon
    Lv 7
    8 months ago

    The first stage is finding x...

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  • 8 months ago

    By the Pythagorean Theorem, 7^2 + 24^2 = 25^2, so if sin(x) = 7/25, cos(x) = 24/25. sin(3π/2) and cos(3π/2) are easy if you know the unit circle.  Both of the former values will stay positive as x is in quadrant 1.  Then utilize this formula: cos(x - y) = cos(x)cos(y) + sin(x)sin(y).

    cos(x - 3π/2)

    = cos(x)cos(3π/2) + sin(x)sin(3π/2)

    = (24/25)(0) + (7/25)(-1)

    = 0 - 7/25

    = -7/25.  Final.

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