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Prove that sine inverse x = cosec inverse 1/x

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  1. Draw the unit circle.
    Draw a right triangle in standard position (right angle on the x-axis).

    Now label the sides.
    The hypotenuse is 1
    The height is x
    Let angle A be at (0,0)

    So, sin(A) = x/1 = x
    That is, A = sin^-1(x)

    csc(A) = 1/sin(A) = 1/x
    So, A = csc^-1(1/x)

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