Suppose tan theta=15pi/18 is less than theta 3pi/2 , what are the other trigonometric functions?

Answer 1

having a hard time parsing

tanθ=15pi/18 < θ 3π/2

Since π seldom appears in the value of trig functions, it sounds like you meant to ask

tanθ = 15/18 and θ < 3π/2

It's still a bit ambiguous, since tanθ > 0 in QI and QIII.

I'll use QI, and you cac decide how to fix things up to solve your realproblem.

If tanθ = 15/18, then you have a right triangle with
y=15
x=18
r=3√61

In that case,

sinθ = y/r = 5/√61
cosθ = x/r = 6/√61
tanθ = y/x = 15/18

Don't know whether that helps, but however your data really work, just set up your triangle and remember that

sinθ = y/r
cosθ = x/r
tanθ = y/x