Calculus is designed for the common - or three-semester common calculus path, incorporating cutting edge good points to reinforce pupil studying. The publication courses scholars during the middle recommendations of calculus and is helping them know how these ideas follow to their lives and the area round them. as a result of the complete nature of the fabric, we're providing the e-book in 3 volumes for flexibility and potency. quantity three covers parametric equations and polar coordinates, vectors, features of numerous variables, a number of integration, and second-order differential equations.
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Extra resources for Calculus
3 2 Polar Curves Now that we know how to plot points in the polar coordinate system, we can discuss how to plot curves. In the rectangular coordinate system, we can graph a function y = f (x) and create a curve in the Cartesian plane. In a similar fashion, we can graph a curve that is generated by a function r = f (θ). 2 Chapter 1 | Parametric Equations and Polar Coordinates 49 The general idea behind graphing a function in polar coordinates is the same as graphing a function in rectangular coordinates.
Finally, connect the points, and take advantage of any patterns that may appear. The function may be periodic, for example, which indicates that only a limited number of values for the independent variable are needed. Problem-Solving Strategy: Plotting a Curve in Polar Coordinates 1. Create a table with two columns. The first column is for θ, and the second column is for r. 2. Create a list of values for θ. 3. Calculate the corresponding r values for each θ. 4. Plot each ordered pair (r, θ) on the coordinate axes.
The 42. x = 3 cos t y = 3 sin t 43. x = 2 cos(3t) y = 2 sin(3t) 45. x = 3 cos t y = 4 sin t 46. x = 2 cos(3t) y = 5 sin(3t) 47. x = 3 cosh(4t) y = 4 sinh(4t) 48. x = 2 cosh t y = 2 sinh t x = h + r cos θ Show that y = k + r sin θ represents the equation of a circle. 50. Use the equations in the preceding problem to find a set of parametric equations for a circle whose radius is 5 and whose center is (−2, 3). For the following exercises, use a graphing utility to graph the curve represented by the parametric equations and identify the curve from its equation.
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