   Chapter 10, Problem 14RE

Chapter
Section
Textbook Problem

# Sketch the polar curve.14. r = 2 cos(θ/2)

To determine

To sketch: The polar curve r=2cosθ2.

Explanation

Given:

The Polar equation for the variable r is as follows.

r=2cosθ2 (1)

To draw the curve for the values of θ and r:

Determine the value of r.

Substitute the value of 0° for θ.

r=(2×cos(0.5×0°)×π180)=2

Similarly substitute till 1080° for θ.

Summarize the values of θ and r as shown in the table (1).

 θ r 0.00 2.00 10.00 1.99 20.00 1.97 30.00 1.93 40.00 1.88 50.00 1.81 60.00 1.73 70.00 1.64 80.00 1.53 90.00 1.41 100.00 1.29 110.00 1.15 120.00 1.00 130.00 0.85 140.00 0.68 150.00 0.52 160.00 0.35 170.00 0.17 180.00 0.00 190.00 -0.17 200.00 -0.35 210.00 -0.52 220.00 -0.68 230.00 -0.85 240.00 -1.00 250.00 -1.15 260.00 -1.29 270.00 -1.41 280.00 -1.53 290.00 -1.64 300.00 -1.73 310.00 -1.81 320.00 -1.88 330.00 -1.93 340.00 -1.97 350.00 -1.99 360.00 -2.00 370.00 -1.99 380.00 -1.97 390.00 -1.93 400.00 -1.88 410.00 -1.81 420.00 -1.73 430.00 -1.64 440.00 -1.53 450.00 -1.41 460.00 -1.29 470.00 -1.15 480.00 -1.00 490.00 -0.85 500.00 -0.68 510.00 -0.52 520.00 -0.35 530.00 -0.17 540.00 0.00 550.00 0.17 560.00 0.35 570.00 0.52 580.00 0.68 590.00 0.85 600.00 1.00 610.00 1.15 620.00 1.29 630.00 1.41 640.00 1.53 650.00 1.64 660.00 1.73 670.00 1.81 680.00 1.88 690.00 1.93 700.00 1.97 710.00 1.99 720.00 2.00 730.00 1.99 740.00 1.97 750.00 1.93 760.00 1.88 770.00 1.81 780.00 1.73 790.00 1.64 800.00 1.53 810.00 1.41 820.00 1.29 830.00 1.15 840.00 1.00 850.00 0.85 860.00 0.68 870.00 0.52 880.00 0.35 890.00 0.17 900.00 0.00 910.00 -0.17 920.00 -0.35 930.00 -0.52 940.00 -0.68 950.00 -0.85 960.00 -1.00 970.00 -1.15 980.00 -1.29 990.00 -1.41 1000.00 -1.53 1010.00 -1.64 1020.00 -1.73 1030.00 -1.81 1040.00 -1.88 1050.00 -1.93 1060.00 -1.97 1070.00 -1.99 1080.00 -2.00

Graph:

Draw the polar curve for the values of θ and r as shown in the figure (1) from table 1

To draw the curve for the values of x and y.

Determine the value of x:

x=rcosθ

Substitute the value of 1 for r and 0° for θ.

x=2×cos0°=2

Determine the value of y.

y=rsinθ

Substitute the value of 1 for r and 0° for θ.

y=2×sin0°=0

Summarize the values of θ,r,x and y as shown in the table (2).

 θ r x y 0.00 2.00 2

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