Chapter 10: Q. 24. (page 694)

In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.
$x = c s c t, y = c o t t; \frac{π}{4} \leq t \leq \frac{π}{2} .$

Short Answer

Expert verified

The equation is $x^{2} - y^{2} = 1 .$

Step by step solution

Step 1. Given information.

$x = c s c t, y = c o t t$ is given.

Step 2. Form the graph and equation.

we form the rectangular equation by eliminating t in the equation-

$x = c s c t y = c o t t c s c^{2} t = 1 + c o t^{2} t x^{2} = 1 + y^{2} x^{2} - y^{2} = 1 .$

Graph the curve defined by the parametric equations -

$t$	$x$	$y$	$(x, y)$
$\frac{π}{4}$	$\sqrt{2}$	$1$	$(\sqrt{2}, 1)$
$\frac{π}{2}$	$1$	$0$	$(1, 0)$

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In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.
$x = c s c t, y = c o t t; \frac{π}{4} \leq t \leq \frac{π}{2} .$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Form the graph and equation.

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In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.x=csct,y=cott;π4≤t≤π2.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Form the graph and equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Geometry

Mechanics Maths

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In problem graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. Verify your graph using a graphing utility.
$x = c s c t, y = c o t t; \frac{π}{4} \leq t \leq \frac{π}{2} .$