trigonometry

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why does supplementary angles always have the same sin?

  • trigonometry -

    use the difference formula:

    sin(π-x) = sinπ cosx - cosπ sinx

    sinπ=0 and cosπ = -1, so you wind up with

    0 - (-1)(sinx) = sinx

    Also, if you draw the angles in standard position, recall that

    sinθ = y/r
    cosθ = x/r

    since y is positive in QI and QII, the two angles have the same sine value.

    This also shows why cos(π-x) = -cosx -- x is negative in QII.

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