Of the six trig functions how many need to be defined before

Of the six trig functions, how many need to be defined before all six are determined through functional relationships? Please show work and explain.

Solution

If we can define even one trigonometric function we can get rest of five.

example : we have sin(x) function given:

so we can find from relation : cosx = sqrt( 1- sin^2x)

tanx = sinx/cosx

Now we can find cscx = 1/sinx

secx = 1/cosx

cotx = 1/tanx

So, we have all six trig functions