Convert between 11.4 polar coordinates and rectangular 19. Rewrite the polar equation r = 6 sin(e) as a Cartesian equation. coordinates Graph functions 11.5 20. Draw the following polar graphs in polar coordinates Find points of 11.5 intersection of a) r = 4 - 4 sin b) r = 5 sin(20) 21. Find the points of intersection of the following polar curves r = 6 cos(20) and r = 3 polar graphs Convert complex 11.7 numbers to polar form Multiply, divide 11.7 and use exponents on complex numbers in polar form Find roots of 11.8 complex numbers in polar form Perform operations on vectors such as: 22. Convert the following complex number in polar (cis) form z=1-3i 23. For the two complex numbers: z = 2 + 2i and z = 4i Convert each to polar form. Find the following: a) ZZ2 b) 21 c) z 24. For the complex numbers: z = -4-4i Find the z 11.8 25. b Let a (4,-2) and 6 = (-3, 3). Find 3 - b. = addition and scalar multiplication. Find magnitude 11.8 26. and angle orientation of vectors Find dot product 11.9 and angle between vectors Write equations 11.10 in parametric form and graph equations in parametric form a) For the following vector, convert from magnitude and direction to x and y coordinates r = 5,0 = 330 b) For the following vector, convert from x and y coordinates to magnitude and direction 27. Let a (-7,-6) and 6 = (-8, 7). Compute the dot product. Then find the angle between the two vectors. 28. For the following parametric equations (x(t)=6t ly(t)=8t+7 t0 a) Make a table of values showing several values of t, x and y. b) Plot the parametric equations by hand. Be sure to indicate the orientation of the curve on the graph. c) Solve for y as a function of x, y = f(x).