The terminal side of #theta# in standard position contains (5,12), how do you find the exact values of the six trigonometric functions of #theta#?

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Answer 1 · 2017-04-01T06:41:34

#sin theta=12/13#, #cos theta=5/13#, #tan theta=12/5#

#csc theta=13/12#, #sec theta=13/5#, #cot theta=5/12#

Let #(x,y)=(5,12)#.

#r=sqrt{x^2+y^2}=sqrt(5^2+12^2)=13#

By definition,

#sin theta=y/r=12/13#

#cos theta=x/r=5/13#

#tan theta=y/x=12/5#

#csc theta=r/y=13/12#

#sec theta=r/x=13/5#

#cot theta=x/y=5/12#

I hope that this was clear.