Q 7. - Calculus

Question

Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.

$x=\sin h t$, $y=\cos h t$, $t\in \mathfrak{R}$.

Step-by-Step Solution

Answer

The solution is:

Step 1. Given information.

Given parametric equations are $x=\sin h t$ and $y=\cos h t$.

Step 2. Find the values of x and y .

_{We know that:}

_{$\cos h^{2}t-\sin h^{2}t=1$}

_{Also, it is given that $y=\cos h t$ and $x=\sin h t$.}

_{So, the required equation is:}

_{$\begin{array}{rcl}\cos h^{2}t-\sin h^{2}t& =& 1\\ y^2-x^2& =& 1\end{array}$}

Step 3. Draw the graph of the given parametric equations.

Simply use a graphing calculator to draw a graph of $y^2-x^2=1$.

The required graphical representation is: