The following image shows my confusion:
I don't have any trouble doing the derivative, but how did they arrive from the second-last line to the last?
I know that sin^2(x) + cos^2(x) = 1, but I can't see how to relate that here.
The following image shows my confusion:
I don't have any trouble doing the derivative, but how did they arrive from the second-last line to the last?
I know that sin^2(x) + cos^2(x) = 1, but I can't see how to relate that here.
Since you were told that $\displaystyle {\color{red}x}={\color{red}r\cos\theta}$ and $\displaystyle {\color{blue}y}={\color{blue}r\sin\theta}$, we see that:
$\displaystyle y\left(-{\color{blue}r\sin\theta}\right)+x\left({\color{re d}r\cos\theta}\right)=y\left(-{\color{blue}y}\right)+x\left({\color{red}x}\right )=x^2-y^2$