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Find y if the point (5,y) is on the terminal side of theta and cos theta = 5/13

User Knitschi
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For this problem we have a point given (5,y) and we know that this point is on a terminal side of an angle, we also know that:


\cos \theta=(5)/(13)

If we know the cos then we can find the sin on this way:


\sin \theta=(y)/(13)

Then we can apply the following identity from trigonometry:


\sin ^2\theta+\cos ^2\theta=1

Using this formula we got:


((5)/(13))^2+((y)/(13))^2=1

And we can solve for y:


(y^2)/(169)=1-(25)/(169)=(144)/(169)

And solving for y we got:


y=\sqrt{169\cdot(144)/(169)}=√(144)=\pm12

And the two possible solutions for this case are y=12 and y=-12

User Chaoss
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