Trig

Find sec theta if sin theta = -4/5 and 270 degrees < theta < 360 degrees.

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  1. sin theta = -4/5 , so y=-4, r = 5

    then r^2 = x^2 + y^2
    25 = x^2 + 16
    x = ±3 , but we are in quadrant IV, so x = +3
    then cos theta = 3/5
    and
    sec theta = 5/3

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  2. We are talking a 3,4,5 right triangle here in the fourth quadrant.
    Draw it
    opposite down to the right 4 units
    hypotenuse 5
    adjacent from origin to x = +3
    so
    cos Theta = 3/5
    sec T = 1/cos T = 5/3

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