What is the general solution for 3sin^2(x)-2sin(x)-5=0 ?

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

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3sin^2(x)-2sin(x)-5=0

3 sin^{2} (x) - 2 sin (x) - 5 = 0

x = \frac{3 π}{2} + 2 πn

Solution steps

3 sin^{2} (x) - 2 sin (x) - 5 = 0

Solve by substitution

sin (x) = \frac{5}{3}, sin (x) = - 1

sin (x) = \frac{5}{3} :

No Solution

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

- 2 cos (x) + 4 cos (2 x) = 0

2 tan^{2} (x) - 9 tan (x) + 7 = 0

\frac{1}{2} = cos^{2} (x)

cos (A) = \frac{1}{2}

3 sin^{2} (x) - sin (x) = 0

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