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#