The point #(8,15)# is on the terminal side of an angle in standard position, how do you determine the exact values of the six trigonometric functions of the angle?

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Answer 1 · 2017-03-04T17:32:12

#sin theta = 15/17; cos theta = 8/17#
#tan theta = 15/8; cot theta = 8/15#
#csc theta = 17/15; sec theta = 17/8#

Draw a right triangle in the first quadrant of the rectangular coordinate plane with base = #8# and height = #15#.

Calculate the hypotenuse using Pythagorean Theorem:
#r = sqrt (8^2 + 15^2) = sqrt(64 + 225+ = sqrt(289) = 17#

Use the trig. definitions to find all of the angles:
#sin theta = "opposite"/"hypotenuse" = 15/17#

#cos theta = "adjacent"/"hypotenuse" = 8/17#

#tan theta = "opposite"/"adjacent" = 15/8#

#csc theta = 1/(sin theta) = 17/15#

#sec theta = 1/(cos theta) = 17/8#

#cot theta = 1/(tan theta) = 8/15#