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 · 2017-08-16T16:31:52

Please see below.

Memorize this

#(x,y)# lies on the terminal side of #theta#, then

#r = sqrt(x^2+y^2)# and

#sin theta = y/r# #" "# #" "# #" "# #csc theta = r/y#

#cos theta = x/r# #" "# #" "# #" "# #sec theta = r/x#

#tan theta = y/x# #" "# #" "# #" "# #cot theta = x/y#

For this question

We have #(x,y) = (8,-15)#
Do the arithmetic and substitute.

#r = sqrt((8)^2+(-15)^2) = 17#

So

#sin theta = -15/17# #" "# #" "# #" "# #csc theta =-17/15#

#cos theta = 8/17# #" "# #" "# #" "# #sec theta = 17/8#

#tan theta = -15/8# #" "# #" "# #" "# #cot theta = -8/15#