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

The general solution for 2cos^2(θ)=3sin(θ) is θ= pi/6+2pin,θ=(5pi)/6+2pin

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2cos^2(θ)=3sin(θ)

2 cos^{2} (θ) = 3 sin (θ)

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Solution steps

2 cos^{2} (θ) = 3 sin (θ)

Subtract

3 sin (θ)

from both sides

2 cos^{2} (θ) - 3 sin (θ) = 0

Rewrite using trig identities

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

Solve by substitution

sin (θ) = - 2, sin (θ) = \frac{1}{2}

sin (θ) = - 2 :

No Solution

sin (θ) = \frac{1}{2} : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Combine all the solutions

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

sin^{2} (θ) = 8 sin (θ) + 9

x, e^{c o s (y)} = cos (x)

10 sin (3 x) = 5

4 0^{2} = 2 8^{2} + 1 5^{2} - 2 (28) (15) \cdot cos (x)

5 tan^{2} (x) - 1 = 2 tan^{2} (x)

What is the general solution for 2cos^2(θ)=3sin(θ) ?
The general solution for 2cos^2(θ)=3sin(θ) is θ= pi/6+2pin,θ=(5pi)/6+2pin