Chapter 9: Q. 23 (page 721)

In Exercises 16–23 sketch the parametric curve by plotting points.
23. $x = \cos^{5} t, y = \sin^{5} t, t \in [0, 2 π]$

Short Answer

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Given information

Given : $x = \cos^{5} t, y = \sin^{5} t, t \in [0, 2 π]$

:Substituting different values in the parametric equations

Find the values of $x, y$ by substituting different values in the parametric equations :

(a) When $t = 0$ , the point $(x, y)$ is :

$(x, y) = (\sin^{5} t, \cos^{5} t) = (\sin^{5} 0, \cos^{5} 0) . . . (\sin c e t = 0) = (0, 1)$

(b) When $t = π$ $(x, y)$ is :

$(x, y) = (\sin^{5} t, \cos^{5} t) = (\sin^{5} π, \cos^{5} π) . . . [b y i n s e r t i n g t = π], = (0, - 1)$

:Substituting different values in the parametric equations

$(x, y) = (\sin^{5} t, \cos^{5} t) = (\sin^{5} \frac{3 π}{2}, \cos^{5} \frac{3 π}{2}) . . . (\sin c e t = \frac{3 π}{2}) = (- 1, 0)$

Plotting graph

The required graph is :

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In Exercises 16–23 sketch the parametric curve by plotting points.
23. $x = \cos^{5} t, y = \sin^{5} t, t \in [0, 2 π]$

Short Answer

Step by step solution

Given information

:Substituting different values in the parametric equations

:Substituting different values in the parametric equations

Plotting graph

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In Exercises 16–23 sketch the parametric curve by plotting points.23.x=cos5t,y=sin5t,t∈[0,2π]

Short Answer

Step by step solution

Given information

:Substituting different values in the parametric equations

:Substituting different values in the parametric equations

Plotting graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Theoretical and Mathematical Physics

Decision Maths

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

In Exercises 16–23 sketch the parametric curve by plotting points.
23. $x = \cos^{5} t, y = \sin^{5} t, t \in [0, 2 π]$