Chapter 9: Q 7. (page 775)

Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.
$x = \sin h t$ , $y = \cos h t$ , $t \in R$ .

Short Answer

Expert verified

The solution is:

Step by step solution

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:

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Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.
$x = \sin h t$ , $y = \cos h t$ , $t \in R$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the values of x and y.

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

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Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.x=sinht,y=cosht,t∈R.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the values of x and y.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Mechanics Maths

Decision Maths

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.
$x = \sin h t$ , $y = \cos h t$ , $t \in R$ .