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Calculus/using trig identities

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Expert: - 1/31/2010


Question
In each case, find sin(α), cos(α), tan(α), csc(α), sec(α), and cot(α).
sin(2α) = -15/17 and 180° < 2α < 270°"

Answer
Since the sin(2α) is -15/17 and 2α is in the III quadrant, that makes the other side negative as well.  It should also be noted that 17² - 15² = 289 - 225 = 64 = 8², so the other side is -8.

That makes cos(2α) = -8/17.  Knowledge of sin(2α) and cos(2α) are enough to find all six trig functions on α.  Here are the formulas needed: sin(α) = √([1-cos(2α)]/2),
cos(α) = √([1+cos(2α)]/2), tan(α) = [1-cos(2α)]/sin(2α).

Once these have been found, sec(α) = 1/cos(α), csc(α) = 1/sin(α), and ctn(α) = 1/tan(α).

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