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9.45.) (a) Use the figure to show that x =r cos ø, y = r sin ø and x' = r cos( ø – 0),y' = r sin (4 – 0). P(x, y) or P(x', y') FIGURE 7.4.6 Rotated axes in Problem 36 (b) Use the results from part (a) to derive the rotation equations: x' = x cos 0+ y sin 0 y' = -x sin 0 + y cos 0 (c) Use x' = x cos 0+ y sin 0 and y' = -x sin 0 + y cos 0 to find rotation equations in: x = x' cos 0 – y' sin 0 y = x' sin 0 – y' cos 0

9.45.) (a) Use the figure to show that x =r cos ø, y = r sin ø and x' = r cos( ø – 0),y' = r sin (4 – 0). P(x, y) or P(x', y') FIGURE 7.4.6 Rotated axes in Problem 36 (b) Use the results from part (a) to derive the rotation equations: x' = x cos 0+ y sin 0 y' = -x sin 0 + y cos 0 (c) Use x' = x cos 0+ y sin 0 and y' = -x sin 0 + y cos 0 to find rotation equations in: x = x' cos 0 – y' sin 0 y = x' sin 0 – y' cos 0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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9.45.) (a) Use the figure to show that x =r cos ø, y =r sin ø and x' = r cos( ø– 0),y' = r sin (4 –- 0). P(x, y) or P(x', y') FIGURE 7.4.6 Rotated axes in Problem 36 (b) Use the results from part (a) to derive the rotation equations: x' = x cos 0+ y sin 0 y' = -x sin 0 + y cos 0 (c) Use x' = x cos 0+ y sin 0 and y' = -x sin 0 + y cos 0 to find rotation equations in: x = x' cos 0 – y' sin 0 y = x' sin 0 – y' cos 0
Transcribed Image Text:9.45.) (a) Use the figure to show that x =r cos ø, y =r sin ø and x' = r cos( ø– 0),y' = r sin (4 –- 0). P(x, y) or P(x', y') FIGURE 7.4.6 Rotated axes in Problem 36 (b) Use the results from part (a) to derive the rotation equations: x' = x cos 0+ y sin 0 y' = -x sin 0 + y cos 0 (c) Use x' = x cos 0+ y sin 0 and y' = -x sin 0 + y cos 0 to find rotation equations in: x = x' cos 0 – y' sin 0 y = x' sin 0 – y' cos 0
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