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?

Question

45728 views around the world

You can reuse this answer
Creative Commons License

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#