<s>[INST] Cannot understand trig manipultion $a$ is a radius in a origin centered circle.
Any point on a circle circumference has coordinates $(a\ \cos\theta, a \ \sin\theta)$. 
I do not understand the last transformation in this expression $x = \sqrt{a^2 - y^2} = \sqrt{a^2 - a^2 \sin^2\theta } = a \cos\theta $ 
How do we get $ \sqrt{a^2 - a^2 \sin^2\theta } = a \cos\theta $ ???
Note: this is just a part of calc lecture in MIT ocw
 [/INST] $$ \sqrt{ a^2 - a^2 \sin^2 \theta } $$
$$ = \sqrt{ a^2 ( 1 - \sin^2 \theta ) } $$
$$ = a \sqrt{ \cos^2 \theta } $$
$$ = a \cos \theta $$
We can simplify $1-\sin^2\theta$, because of the pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$.
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