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Home Trigonometric Functions Slopes And Curve Sketching in Polar Coordinates Sketching Trigonometric Functions in Polar Coordinates.
 
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Sketching Trigonometric Functions in Polar Coordinates.

Polar coordinates are best suited for trigonometric functions, which have the property that f(θ) = f(θ + 2π). We shall therefore concentrate on the interval

0 ≤ θ < 2π.

Suppose that the function r = f(θ) is differentiate for 0 ≤ θ ≤ 2π. The following steps may be used in sketching the curve.

Step 1

Compute dr/dθ.

Step 2

Find all points where r = 0 or dr/dθ = 0.

Step 3

Sketch y = f(x) in rectangular coordinates. (A method for doing this is given in Section 3.9.)

Step 4

Compute r, dr/dθ, and tan ψ = r(dr/dθ) at the points where r = 0 or dr/dθ = 0 and at least one point between. Make a table, and test for local maxima or minima.

Step 5

Draw a smooth curve using the rectangular graph of step three and the table of step four.

Home Trigonometric Functions Slopes And Curve Sketching in Polar Coordinates Sketching Trigonometric Functions in Polar Coordinates.

Last Update: 2006-11-05