How do you find the exact values of the six trigonometric function of #theta# if the terminal side of #theta# in the standard position contains the point (4,4)?

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Answer 1 · 2017-01-25T04:18:41

First identify this as a 45-45-90 degree triangle. From there, the ratios can be found (see below):

We have a #45^o# angle in Q1:

45-45-90 triangles have a ratio of sides of 1, 1, #sqrt2#.

We can now work out the trig ratios:

#sinx="opp"/"hyp"=1/sqrt2=sqrt2/2#

#cosx="adj"/"hyp"=1/sqrt2=sqrt2/2#

#tanx="opp"/"adj"=1/1=1#

#cscx="hyp"/"opp"=sqrt2/1=sqrt2#

#secx="hyp"/"adj"=sqrt2/1=sqrt2#

#cotx="adj"/"opp"=1/1=1#