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:

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

We can now work out the trig ratios:

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

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

$tanx="opp"/"adj"=1/1=1$

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

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

$cotx="adj"/"opp"=1/1=1$

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