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tr-t4n-a - NAME Very Brief Answers TEST-04/MAC1114 Page 1...

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NAME: Very Brief Answers TEST-04/MAC1114 Page 1 of 4 Read Me First: Show all essential work neatly. Use correct notation when presenting your computations. Write using complete sentences. In particular, be very careful when using "=", equals , and " ", implies . Do not "box" your answers. Communicate. 1. (15 pts.) Identify each of the following polar equations as completely as possible by transforming each equation to rectangular coordinates. [These are fairly easy!!] (a) θ = -(1/6) π This is the straight line through the origin defined by the equation y = -tan( π /6) x = -3 -1/2 x. (b) 2r sin( θ ) = 3r cos( θ ) This is the straight line through the origin defined by the equation 2y = 3x. (c) r = 3 This is the circle centered at the origin with radius equal to 3. Its rectangular equation is x 2 + y 2 = 9. (d) r = 2 sin( θ ) This is the circle with the following rectangular equation: x 2 + (y - 1) 2 = 1. Consequently, its center is at (0,1) and it has a radius equal to 1. (e) r cos( θ ) = -4 This is simply the line parallel to the x-axis defined by x = -4.
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