[sickufully]

I'm not fully understanding what it's asking me to do here. I do understand the 4th quadrant must have cos𝜃>0 but I'm unsure if I'm applying the following rule correctly (I have no idea for the second one (ii), when tan𝜃<0):

Rule - cos^2𝜃 + sin^2𝜃 = 1



My attempt went something like this for (i):
Cos^2𝜃 + Sin^2𝜃 = 1
Cos^2𝜃 + (-3/5)^2 = 1
Cos^2𝜃 + (9/25) = 1
Cos^2𝜃 + (9/25) - (9/25) = 1 - (9/25)
Cos^2𝜃 = (25/25) - (9/25)
Cos^2𝜃 = (16/25)
Cos𝜃 = sqrt(16/25)
Cos𝜃 = ±sqrt(16/25)
Cos𝜃 = ±(4/5)
Cos𝜃 = 4/5 (because if it's in the 4th quadrant, it has to be positive)

Am I applying the rule correctly or am I way off?