You need to use the rule
sin2(x) + cos2(x) = 1. (this is actually the best rule in Trig, we use it a lot, make sense to know this rule by heart).
If you use it, you able to find a cos (x) if sin(x) is known.
For example, Sinθ=2/5, so sin2(θ)=4/25. so, cos2(θ)=1-4/25=25/25 - 4/25 = 21/25
Tanθ >0 means that sin(θ) and cos(θ) have the same sign, our sin(θ) >0, so cos(θ)>0. Do you understand why?
cos2(θ) = 21/25, so cos(θ) = sqrt(21)/5
and tan(θ) = sin(θ)/cos(θ) = 2/sqrt(21) or 2*sqrt(21)/21 (since we don't like roots in the denominator).
What are the other functions, do you know? Do you need help with calculating the values?
For the next problem we have
sin(θ)/cos(θ) = 2,
so sin(θ) = 2*cos(θ). (multiplying by cos(θ) both sides and remembering that cos(θ) is NOT 0)
if we square both sides, we have
sin2(θ)=4cos2(θ)
Do you remember the rule that we used before in the problem 1? Let's use it again!!
sin2(θ) = 1 - cos2(θ)
1 - cos2(θ) = 4 cos2(θ)
1 = 5 cos2(θ)
could you take it from here?
For the last one, we need a definition of Csc.
And we know that csc x = 1/sin x
so, knowing that Cscθ=-3 we can calculate sin(θ) = -1/3.
Do you need more help? I'm available for online tutoring.
