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Finding exact values for trig functions of acute angles.

I have $\sin \theta = 3/5$.

I know that $y = 3$ and $r = 5$.

How the heck do I get $x$ if I don't know the angle?

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1  
what exactly are x,y,r and $\theta$? – gfes Jun 6 '11 at 1:35
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What are $y$, $r$, and $x$? And how is it you "know" $y$ and $r$? – Arturo Magidin Jun 6 '11 at 1:37
    
y is the opposite and r is the hypotenuse. – Adam Jun 6 '11 at 1:39
    
@Adam: Then you have a right triangle. Pythagoras is your friend (or should be, if you didn't keep snubbing him...) – Arturo Magidin Jun 6 '11 at 1:49
    
Its been 8 years or so since I have had to us it so it is easy to forgot. That or am an an idiot. – Adam Jun 6 '11 at 1:50
up vote 1 down vote accepted

If you know that $y=3$ and $r=5$, then because (presumably) the triangle is a right triangle with legs of length $x$ and $y$, and hypotenuse $r$, by the Pythagorean theorem we have that $$x^2+y^2=r^2,$$ hence $$x^2+9=25.$$ Thus $x^2=16$, and therefore $x=4$.

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You can draw a picture, too. That makes keeping things straight easy.

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