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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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Again, please put some tag in addition to "homework". – Arturo Magidin Jun 6 '11 at 1:34
I don't know how, it won't allow me to create new tags. – Adam Jun 6 '11 at 1:34
what exactly are x,y,r and $\theta$? – gfes Jun 6 '11 at 1:35
@Adam: You don't have to create tags; you just have to use the ones that already exist, like [trigonometry]. List apropriate tags, separated by spaces. – Arturo Magidin Jun 6 '11 at 1:35
What are $y$, $r$, and $x$? And how is it you "know" $y$ and $r$? – Arturo Magidin Jun 6 '11 at 1:37

2 Answers 2

up vote 2 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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