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Home Trigonometric Functions Slopes And Curve Sketching in Polar Coordinates Examples Example 1: Sketching r = 1 + cos θ in Polar Coordinates
 
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Example 1: Sketching r = 1 + cos θ in Polar Coordinates

Sketch the curve

r = 1 + cos θ.

Step 1

dr/dθ = -sin θ.

Step 2

r = 0 when θ = π. dr/dθ = 0 when θ = 0, π.

Step 3

See Figure 7.8.6.

07_trigonometric_functions-470.gif

Figure 7.8.6

Step 4

θ

r = 1 + cos θ

dr/dθ

tan ψ

Comments

0

2

0

-

max

π/2

1

-1

-1

|r| decreasing

π

0

0

-

min, cusp at 0

3π/2

1

1

1

|r| increasing

Step 5

We draw the curve in Figure 7.8.7. The curve is called a cardioid because of its heart shape.

07_trigonometric_functions-471.gif

Figure 7.8.7

Home Trigonometric Functions Slopes And Curve Sketching in Polar Coordinates Examples Example 1: Sketching r = 1 + cos θ in Polar Coordinates

Last Update: 2006-11-15