Question

express root(9+x^2) as a trigonomentric function of tita without using radicals by letting x=3tantita.assume that 0<tita<TT/2 hence find sine tita and cos tita
plz show working thanks

Answer 1

theta, not tita.

let x = 3tanθ

x^2 = 9tan^2θ
9+x^2 = 9+9tan^2θ = 9sec^2θ
√(9+x^2) = 3secθ

so, draw a right triangle. Since tanθ = x/3, those are the two legs, and the hypotenuse is √(9+x^2)

Now you can write down sinθ and cosθ