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

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

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2sin^2(u)-3cos(u)=0

2 sin^{2} (u) - 3 cos (u) = 0

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

Solution steps

2 sin^{2} (u) - 3 cos (u) = 0

Rewrite using trig identities

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

Solve by substitution

cos (u) = - 2, cos (u) = \frac{1}{2}

cos (u) = - 2 :

No Solution

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

Combine all the solutions

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

sin (2 t) = sin (t)

cos (x) = \frac{17.6}{26}

tan (2 θ) = - 2.5

1 + 4 cos (θ) = 3 sin (θ), 0 \leq θ \leq 2 π

\frac{150}{sin ( x )} = \frac{140.78}{sin ( 11 5 ^{\circ} )}

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