What is the general solution for 2sin^2(w)-sin(w)-1=0 ?

The general solution for 2sin^2(w)-sin(w)-1=0 is w= pi/2+2pin,w=(7pi)/6+2pin,w=(11pi)/6+2pin

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2sin^2(w)-sin(w)-1=0

2 sin^{2} (w) - sin (w) - 1 = 0

w = \frac{π}{2} + 2 πn, w = \frac{7 π}{6} + 2 πn, w = \frac{11 π}{6} + 2 πn

Solution steps

2 sin^{2} (w) - sin (w) - 1 = 0

Solve by substitution

sin (w) = 1, sin (w) = - \frac{1}{2}

sin (w) = 1 : w = \frac{π}{2} + 2 πn

sin (w) = - \frac{1}{2} : w = \frac{7 π}{6} + 2 πn, w = \frac{11 π}{6} + 2 πn

Combine all the solutions

w = \frac{π}{2} + 2 πn, w = \frac{7 π}{6} + 2 πn, w = \frac{11 π}{6} + 2 πn

3 sin (x) = 7 cos (x)

8 sin (θ) - 3 = 0

cos^{2} (4 x) - sin^{2} (4 x) = cos (b)

y, sin (x + y) + sin (y + z) + sin (x + z) = 0

2 sin (x) - tan (x) = 0

What is the general solution for 2sin^2(w)-sin(w)-1=0 ?
The general solution for 2sin^2(w)-sin(w)-1=0 is w= pi/2+2pin,w=(7pi)/6+2pin,w=(11pi)/6+2pin