Find \sin x \text{ and } \cos x knowing \tan

siutulysr5

siutulysr5

Answered question

2022-01-28

Find sinx  and  cosx knowing tanx
I know tanx=22. How to find sinx and cosx if x[π2,0]? They probably would be 223  and  13 respectively but I don't know how to prove it.

Answer & Explanation

bekiffen32

bekiffen32

Beginner2022-01-29Added 8 answers

We know the signs.
We have
sinx=22cosx
and
sin2x+cos2x=1
Substitute the first equation into the second, and you can solve for cosx. Remember cosx>0 in this quadrant. After that you should be able to recover sinx using the first equation.

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