Mathematics

The key is to find $\frac{dy}{dx}$ using the chain rule: $\frac{dy}{dx} = \frac{dy/dt}{dx/dt}$. You'll need to differentiate both $x$ and $y$ with respect to $t$ using the product rule, then evaluate both derivatives at $t = \frac{\pi}{4}$. The trigonometric values at this angle are simple ($\sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}$), so the arithmetic becomes manageable once you've set up the derivatives correctly.

The key is to find $\frac{dy}{dx}$ using the chain rule: $\frac{dy}{dx} = \frac{dy/dt}{dx/dt}$. You'll need to differentiate both $x$ and $y$ with respect to $t$ using the product rule, then evaluate both derivatives at $t = \frac{\pi}{4}$. The trigonometric values at this angle are simple ($\sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}$), so the arithmetic becomes manageable once you've set up the derivatives correctly.