MA211 Week 2 Tutorial Solution (Repaired) - MA211 Week 2...

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1 Contact: [email protected] MA211 Week 2 Tutorial Solution 1/2017 MA211 Week 2 Tutorial Solution Section 10.2 Polar Coordinates 5b. (-5,0) Let’s first get r . 2 2 2 2 ( 5) 0 25 5 r x y Now, let’s get . 1 1 0 tan tan (0) 0 5 This is not the correct angle however. This value of is in the first quadrant and the point we’ve been given is in the third quadrant. The correct angle is by adding onto this. Therefore, the actual angle is, 0 OR look at the graph of (-5,0). Thus, For 0,0 2 :in polar coordinates the point is (-5,0)=(r, )=(5, ) r For 0, 2 0:in polar coordinates the point is (-5,0)=(r, )=(5,- ) r 5b. 2 3, 2 Let’s first get r . 2 2 2 2 (2 3) ( 2) 16 4 r x y   Now, let’s get . 1 1 2 3 tan tan 3 2 3 The correct angle is
2 Contact: [email protected] MA211 Week 2 Tutorial Solution 1/2017 3 11 , 2 3 6 2 3 6   OR look at the graph of 2 3, 2 . Thus, For 0,0 2 :in polar coordinates the point is 11 (2 3,-2)=(r, )=(4, ) 6 r For 0, 2 0:in polar coordinates the point is (-2 3,-2)=(r, )=(4,- ) 6 r 9a. r=2, this is the equation of a circle of radius 2 centered at the origin. Note: . r a This equation is saying that no matter what angle we’ve got the distance from the origin must be a . If you think about it that is exactly the definition of a circle of radius a centered at the origin. To convert, we use the relationship 2 2 2 2 2 Polarequation 2 2 2 (circleequation)Rectangular Equation r r x y 9c) 3cos r This is a circle 2 cos r a of radius a and center ( ,0). a 2 2 2 2 2 2 2 3cos 3 cos 3 3 0 3 9 (completing the square) 2 4 r r r x y x x x y x y Equation of a circle of radius 3 2 r centered at 3 ,0 2 . 12 a) 3 sin 3, note that sin . y r y r      c) 2 2 2 2 2 2 4 0 4 cos 0, note that and cos . x y x r r r x y x r
3 Contact: [email protected] MA211 Week 2 Tutorial Solution 1/2017 22) 3 4   . This is a line that goes through the origin and makes an angle of 3 4 with the positive x -axis. 24) 4cos , r This is a circle 2 cos r a of radius a and center ( ,0). a Equation of a circle of radius 2 r centered at 2,0 . 26) 2 2cos 2 2cos , r r This is a cardioid cos r a a . A graph that is vaguely heart

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