How do you use the point (15,-8) on the terminal side of the angle to evaluate the six trigonometric functions?

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How do you use the point (15,-8) on the terminal side of the angle to evaluate the six trigonometric functions?

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Answer 1 · 2017-12-18T01:07:27

Find trig functions by using trig identities.
Point (15, -8) is in Quadrant 4.
$tan t = \frac{y}{x} = - \frac{8}{15}$ $tan t = y/x = - 8/15$
$cot t = - \frac{15}{8}$ $cot t = - 15/8$
Find cos t by the identity:
${cos}^{2} t = \frac{1}{1 + {tan}^{2} t} = \frac{1}{1 + \frac{64}{225}} = \frac{225}{289}$ $cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 64/225) = 225/289$
$cos t = \frac{15}{17}$ $cos t = 15/17$ (because t is in quadrant 4)
Find sin t by the identity:
${sin}^{2} t = \frac{1}{1 + {cot}^{2} t} = \frac{1}{1 + \frac{225}{64}} = \frac{64}{289}$ $sin^2 t = 1/(1 + cot^2 t) = 1/(1 + 225/64) = 64/289$
$sin t = - \frac{8}{17}$ $sin t = - 8/17$ (because t is in Quadrant 4)
$sec t = \frac{1}{cos t} = \frac{17}{15}$ $sec t = 1/cos t = 17/15$
$csc t = \frac{1}{sin t} = \frac{17}{8}$ $csc t = 1/sin t = 17/8$

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How do you use the point (15,-8) on the terminal side of the angle to evaluate the six trigonometric functions?

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