PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Expert Solution & Answer
Chapter 8.4, Problem 9E
Solution
To find: The equation used to convert an equation in terms of (x,y) to an equation in terms of (u, v) when the angle of rotation is π6 .
The liner equation is x=√3u2−v2 and y=u2+√3v2 .
Given Information:
The axis of rotation is θ=π6 .
Formula:
The equations for the axis rotation are,
x=ucosθ−vsinθy=usinθ+vcosθ
Calculation:
Substitute π6 for θ in above equation to find the equation in terms of x .
x=ucos(π6)−vsin(π6)=u⋅√32−v⋅12=√3u2−v2
Similarly, substitute π6 for θ in above equation to find the equation in terms of y .
y=usin(π6)+vcos(π6)=u⋅12+v⋅√32=u2+√3v2
Therefore, the required equations are x=√3u2−v2 and y=u2+√3v2 .
Chapter 8 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
Ch. 8.1 - Prob. 1QRCh. 8.1 - Prob. 2QRCh. 8.1 - Prob. 3QRCh. 8.1 - Prob. 4QRCh. 8.1 - Prob. 5QRCh. 8.1 - Prob. 6QRCh. 8.1 - Prob. 7QRCh. 8.1 - Prob. 8QRCh. 8.1 - Prob. 9QRCh. 8.1 - Prob. 10QR
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