hw7sol

# hw7sol - HW 7 Solutions Math 1920 Problem 10.5.30...

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Unformatted text preview: HW 7 Solutions Math 1920 March 10, 2009 Problem 10.5.30 Substitute x = r cos( θ ) and y = r sin( θ ) to get y = x . Line with slope m =- 1 and intercept b = 0. Problem 10.5.36 We have r = 4tan( θ ) sec ( θ ) = 4( sin( θ ) cos 2 ( θ ) ) and therefore r cos 2 ( θ ) = 4sin( θ ) and r 2 cos 2 ( θ ) = 4 r sin( θ ). Now substitute x = r cos( θ ) and y = r sin( θ ) and get y = 4 x 2 , a parabola with vertex (0 , 0) which opens upward. Problem 10.5.41 Substitute x = r cos( θ ) and x 2 + y 2 = r 2 into r 2 =- 4 r cos( θ ). That gives x 2 + y 2 =- 4 x ⇒ x 2 +4 x + y 2 = 0 ⇒ ( x +2) 2- 4+ y 2 = 0 ⇒ ( x +2) 2 + y 2 = 2 2 . A circle with center C(- 2 , 0) and radius 2. Problem 10.5.53 Substitute r 2 = x 2 + y 2 and get r 2 = 4 which gives r = 2 or r =- 2. The two equations produce the same graph. Problem 10.5.54 Substitute r cos( θ ) = x and r sin( θ ) = y into x 2- y 2 = 1 and get r 2 cos 2 ( θ )- r 2 sin 2 ( θ ) = 1 ⇒ r 2 ( cos 2 ( θ )- sin 2 ( θ )) = 1 ⇒ r 2 cos (2 θ ) = 1. Problem 10.6.33 We have r = 2sin( θ ) and r = 2sin(2 θ ) ⇒ sin ( θ ) = sin (2 θ ) = 2 sin ( θ ) cos ( θ ) ⇒ sin ( θ )- 2 sin...
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hw7sol - HW 7 Solutions Math 1920 Problem 10.5.30...

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