Question

If 2sin²θ = 3cosθ, where 0 ≤ θ ≤ 2π, then θ = ______ 

Options

• `pi/6, (7pi)/6`

• `pi/3, (5pi)/3`

• `pi/3, (7pi)/3`

• `(-2pi)/3, (-7pi)/3`

Answer 1

If 2sin²θ = 3cosθ, where 0 ≤ θ ≤ 2π, then θ = `underline(pi/3, (5pi)/3)`.

Explanation:

2sin²θ = 3cosθ

⇒ `2 - 2cos^2theta = 3costheta`

⇒ `2cos^2theta + 3costheta - 2 = 0`

⇒ `costheta = (-3 ± sqrt(9 + 16))/4 + (-3 ± 5)/4`

Neglecting(-) sign, we get

`costheta = 1/2 = cos(pi/3) ⇒ theta = 2npi ± pi/3`

The values of θ between 0 and 2π are `underline(pi/3, (5pi)/3)`.