What is the general solution for 2sin^2(θ)-3cos(θ)=0 ?

The general solution for 2sin^2(θ)-3cos(θ)=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin

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2sin^2(θ)-3cos(θ)=0

2 sin^{2} (θ) - 3 cos (θ) = 0

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solution steps

2 sin^{2} (θ) - 3 cos (θ) = 0

Rewrite using trig identities

(1 - cos^{2} (θ)) \cdot 2 - 3 cos (θ) = 0

Solve by substitution

cos (θ) = - 2, cos (θ) = \frac{1}{2}

cos (θ) = - 2 :

No Solution

cos (θ) = \frac{1}{2} : θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Combine all the solutions

θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

\frac{1}{2} = sin (2 x)

sin (θ) = 0.4

cos (x) = 3 sin (x)

2 sin (x) = cot (x)

12 cos^{2} (θ) = 3

What is the general solution for 2sin^2(θ)-3cos(θ)=0 ?
The general solution for 2sin^2(θ)-3cos(θ)=0 is θ= pi/3+2pin,θ=(5pi)/3+2pin