What is the general solution for 2sin^2(x)+sin(x)-6=0 ?

The general solution for 2sin^2(x)+sin(x)-6=0 is No Solution for x\in\mathbb{R}

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2sin^2(x)+sin(x)-6=0

2 sin^{2} (x) + sin (x) - 6 = 0

No Solution for x \in R

Solution steps

2 sin^{2} (x) + sin (x) - 6 = 0

Solve by substitution

sin (x) = \frac{3}{2}, sin (x) = - 2

sin (x) = \frac{3}{2} :

No Solution

sin (x) = - 2 :

No Solution

Combine all the solutions

No Solution for x \in R

tan (θ) = \frac{8}{15}, sin (θ) > 0

cos (x) = \frac{86.6}{100}

- 2 cos^{2} (θ) - 8 cos (θ) - 1 = - 5 cos (θ)

- 6 sin (θ) = - 33

2 sin (2 x) + cos (x) = 0

What is the general solution for 2sin^2(x)+sin(x)-6=0 ?
The general solution for 2sin^2(x)+sin(x)-6=0 is No Solution for x\in\mathbb{R}