How do you use the point (-12,-15) on the terminal side of the angle to evaluate the six trigonometric functions?

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How do you use the point (-12,-15) on the terminal side of the angle to evaluate the six trigonometric functions?

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Answer 1 · 2018-05-29T00:19:58

Call t the angle whose terminal side passes through point (-12/15).
t lies in Quadrant 3.
We have:
$tan t = y/x = -15/- 12 = 5/4$
$cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 25/16) = 16/41$
$cos t = - 4/sqrt41$ (t in Q. 3 --> cos t is negative)
$sin^2 t = 1 - cos^2 t = 1 - 16/41 = 25/41$
$sin t = - 5/sqrt41$ (t lies in Q. 3 --> sin t is negative)
$tan t = 5/4$
$cot = 4/5$
$sec t = 1/(cos) = - sqrt41/4$
$csc t = - sqrt41/5$

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How do you use the point (-12,-15) on the terminal side of the angle to evaluate the six trigonometric functions?

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