What is the general solution for sin^2(x)+3sin(x)+7=5 ?

The general solution for sin^2(x)+3sin(x)+7=5 is x=(3pi)/2+2pin

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sin^2(x)+3sin(x)+7=5

sin^{2} (x) + 3 sin (x) + 7 = 5

x = \frac{3 π}{2} + 2 πn

Solution steps

sin^{2} (x) + 3 sin (x) + 7 = 5

Solve by substitution

sin (x) = - 1, sin (x) = - 2

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

sin (x) = - 2 :

No Solution

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

cos (2 x) = - 0.6, - 18 0^{\circ} \leq x \leq 18 0^{\circ}

23 cos (\frac{θ}{2}) = - 3

\frac{1}{cos ^{2} ( \frac{θ}{2} )} = 12 cos (θ)

3 cos (x) - sin (x) = 2

cos (x) = \frac{34}{70}

What is the general solution for sin^2(x)+3sin(x)+7=5 ?
The general solution for sin^2(x)+3sin(x)+7=5 is x=(3pi)/2+2pin