First of all, I assume that when you saythat you are actually saying : sec(θ)=5 and tan(θ)=2√6.sec = 5, tan = 2*sqrt(6)
a) Correct. cos(θ)=1/sec(θ)=1/5
b) Correct. cot(θ)=1/tan(θ)=1/(2√6)= √6/12
Assume that 90 is in degrees.
c) cot(90-θ)=tan(θ)= 2√6
sin(θ)= ( 2√6)(1/5)
a) cot(θ)= (√3/3) multiply that by (√3/√3) you get
cot(θ) is u/v, you take it from there? Does your teacher want all possible values of θ or just one?
b) is correct if you are looking for just one value of θ.
hope that helped.