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Prove It Think of the unit circle. If you draw in a radius, it makes an angle $\displaystyle \displaystyle \begin{align*} \theta \end{align*}$ with the positive x-axis. Then draw a segment from the end of the radius to the x-axis, you will have a right-angle triangle. The horizontal length is $\displaystyle \displaystyle \begin{align*} \cos{(\theta)} \end{align*}$ and the vertical length is $\displaystyle \displaystyle \begin{align*} \sin{(\theta)} \end{align*}$. Since it's a right-angle-triangle, Pythagoras' Theorem holds, and so $\displaystyle \displaystyle \begin{align*} \left[ \sin{(\theta)} \right] ^2 + \left[ \cos^2{(\theta)} \right]^2 = 1^2 \end{align*}$, or $\displaystyle \displaystyle \begin{align*} \sin^2{(\theta)} + \cos^2{(\theta)} = 1 \end{align*}$. This is true no matter the value of $\displaystyle \displaystyle \begin{align*} \theta \end{align*}$.