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tr-t4 - NAME TEST-04/MAC1114 Page 1 of 4 Read Me First Show...

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NAME: 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) r = 5 (b) r = 2 cos( θ ) (c) θ = (3/4) π (d) r sin( θ ) = -4 (e) r sin( θ ) = r cos( θ ) 2. (10 pts.) Very carefully sketch the graph of the equation (y + 1) 2 = -4(x - 2) below. y x
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TEST-04/MAC1114 Page 2 of 4 3. (15 pts.) Sketch the given curve in polar coordinates. Do this as follows: (a) Carefully sketch the auxiliary curve, a rectangular graph on the coordinate system provided. (b) Then translate this graph to the polar one. Equation: r = 2 sin(2 θ ) (a) r θ (b) y x 4. (10 pts.) Write each expression in the standard form a + bi. (a) (4 + 5i) + (-8 +2i) = (b) 13/(5 -12i) = (c) 6i 3 - 4i 5 = (d) (4 + 5i) (-8 +2i) = (e) [4(cos 30° + i sin 30°)] 4 =
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TEST-04/MAC1114 Page 3 of 4 5. (10 pts.) Very carefully sketch the graph of the equation
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