Finding the value of cot0

Question

sec0 = 4 and sin0 > 0

Answer 1

Since sec θ=4>0 and sin θ>0 angle θ sit in first quadrant. By Pythagorean identities tan^2 θ+1 = sec^2 θ you can find tan θ which is

tan^2 θ+1 = 4^2

tan^2 θ+1 = 16

tan^2 θ=15

tan θ=√15 (only positive since θ is in first quadrant)

Now using reciprocal identities you can find cot θ =1/tan θ = 1/√15=√15/15

Answer 2

I'm assuming you mean secθ = 4 and sinθ > 0

secθ = 1/cosθ = 4, so cosθ = 1/4 = 0.25

cos^-1(0.25) = 75.52º so θ = 75.52°

cotθ = cot 75.52 = cos 75.52/sin 75.52 = 0.25/0.968 = 0.2582