Understanding Complex Plane and Finding Arguments: A Scientist's Perspective

[SUSUSUSUSUSUSUSU]

Homework Statement

The picture below.

Homework Equations

cos2x=1-2sinx
sin2x= 2sinxcosx

The Attempt at a Solution

I got the modulus by using the Pythagoras theorem which is 2sin theta

But I faced difficulty to find the argument. I have no idea why i end up with tan a (alpha) = cot theta which is not the right answer. on the answer booklet, it's written that it is tan a = -cot theta. I do not understand that why it comes to negative...? I just did tan a = sin2x/(1-cos2x) = cot x. Is it just because it is -isin2x?I think after that i can solve it.

Thank you.

 

[Mark44]

Homework Statement

The picture below.

Homework Equations

cos2x=1-2sinx
sin2x= 2sinxcosx

The Attempt at a Solution

I got the modulus by using the Pythagoras theorem which is 2sin theta

But I faced difficulty to find the argument. I have no idea why i end up with tan a (alpha) = cot theta which is not the right answer.
on the answer booklet, it's written that it is tan a = -cot theta. I do not understand that why it comes to negative...? I just did tan a = sin2x/(1-cos2x) = cot x. Is it just because it is -isin2x?

Yes. The imaginary component is $-\sin(2\theta)$.

I think after that i can solve it.

Thank you.