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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=sinht,y=cosht,t鈭�R.

Short Answer

Expert verified

The solution is:

Step by step solution

01

Step 1. Given information.

Given parametric equations arex=sinhtandy=cosht.

02

Step 2. Find the values of x and y.

We know that:

cosh2t-sinh2t=1

Also, it is given that y=coshtand x=sinht.

So, the required equation is:

cosh2t-sinh2t=1y2-x2=1

03

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

Simply use a graphing calculator to draw a graph ofy2-x2=1.

The required graphical representation is:

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