How do you use $sintheta=1/3$ to find $costheta$ ?

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Answer 1 · 2017-03-09T20:08:50

$costheta=sqrt8/3$

$sintheta="opp"/"hyp"$ , in this case $1/3$ .

Given these values, we can work out the $"adj"$ side of our imaginary triangle to work out $costheta$ which equals $"adj"/"hyp"$ .

$"adj"=sqrt("hyp"^2-"opp"^2)-sqrt(3^2-1^2)=sqrt8$

$costheta="adj"/"hyp"=sqrt8/3$ .

Another way we can work this out is using the trigonometric identity:

$sin^2A+cos^2A-=1$

$cosA-=sqrt(1-sin^2A)$

$costheta=sqrt(1-(1/3)^2)=sqrt(8/9)=sqrt8/3$

How do you use sintheta=1/3sintheta=1/3 to find costhetacostheta?