How do you solve Cos theta Tan theta+sqrt(3)Cos theta=0cosθtanθ+3cosθ=0 for [0,2pi]?

1 Answer

theta = (5pi)/6θ=5π6 and (11pi)/611π6

Explanation:

costheta * (sintheta /costheta) + sqrt3costheta =0cosθ(sinθcosθ)+3cosθ=0

You know that tantheta=sintheta /costhetatanθ=sinθcosθ, which means that you have

sintheta + sqrt3costheta =0sinθ+3cosθ=0

sintheta = - sqrt3 * costhetasinθ=3cosθ

tantheta =-sqrt3tanθ=3 for [0,2pi][0,2π],

theta = pi - (pi/3)θ=π(π3) and 2pi - (pi/3)2π(π3)

theta = (5pi)/6θ=5π6 and (11pi)/611π6