Part 1
Ying is correct while Jabbar is incorrect. The polar form would have cosine listed first, then sine later. The sine term always has the imaginary 'i' attached to it. It's fairly easy to mix these trig functions up. One way to remember is to think alphabetical order (C is before S, cosine before sine). Other than this difference, the two students have identical steps.
==========================================================
Part 2
Ying made the error this time. Jabbar is correct. When using a unit circle, you should find that
cos(pi/2) = 0
sin(pi/2) = 1
The point (x,y) on the unit circle that corresponds to the angle theta will help us see this. Note how x = cos(theta) and y = sin(theta).
Side note: Jabbar now has the correct order of cosine and sine (see part 1 above).
==========================================================
Part 3
Ying made the error of adding the r values. Instead, you should multiply them like Jabbar did. The theta angle values are the terms we add up. An interesting thing to notice is that Ying computed cos(pi/2) = 0, which contrasts to the mistake made in part 2.
==========================================================
Part 4
Ying is correct. You divide the r values, and the order of division is important. The order of division is from left to right. We have 7 on the left and -2 on the right, so that's why Ying ended up with the correct new r value of -7/2. Jabbar swapped the order incorrectly. The same issue shows up when subtracting the theta values. Keep in mind that the order of subtraction is important. Something like 2-3 = -1 is not the same as 3-2 = 1. Ying has the correct order of subtraction for those theta values.
