Chapter 11.1, Problem 6E

To determine

To calculate: The equation which relates x and y directly.

Answer to Problem 6E

The required value of $\frac{dy}{dx}$ is $\sqrt{3}$ .

Explanation of Solution

Given information:

The parametric equations: $x=\sin 6t$ , $y=2t$ for t in the interval $\left[0,\frac{\pi }{2}\right]$

Calculation:

The parametric equations are $x=\sin 6t$ , $y=2t$ .

Rewrite the equation $y=2t$ as:

  $\begin{array}{c}y=2t\\ t=\frac{y}{2}\end{array}$

Substitute $\frac{y}{2}$ in the equation $x=\sin 6t$ .

  $\begin{array}{c}x=\sin 6\left(\frac{y}{2}\right)\\ x=\sin \left(3y\right)\end{array}$

Hence, the required equation is $x=\sin \left(3y\right)$ .