First derivative of a parametric equation

Calculus Level 2

If $x = 3\sin (2\pi t)$ and $y = 6 \cos (2\pi t) ,$ what is the derivative of $y$ with respect to $x$ when $t = \frac18?$

Give your answer to 2 decimal places.

1 solution

July Thomas
May 20, 2016

$\frac{dy}{dx} = \frac{\dot{y}}{\dot{x}}$

For this problem,

$\dot{x} = 6\pi \cos(2\pi t)$

$\dot{y} = -12\pi \sin(2\pi t).$

Hence,

$\frac{dy}{dx} = \frac{-12\pi \sin(2\pi t)}{6\pi \cos(2\pi t)} = -2$