What is the general solution for 2sin^2(x)+7sin(x)=4 ?

The general solution for 2sin^2(x)+7sin(x)=4 is x= pi/6+2pin,x=(5pi)/6+2pin

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2sin^2(x)+7sin(x)=4

2 sin^{2} (x) + 7 sin (x) = 4

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

2 sin^{2} (x) + 7 sin (x) = 4

Solve by substitution

sin (x) = \frac{1}{2}, sin (x) = - 4

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = - 4 :

No Solution

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

22 cos (θ) + 4 = 6

sin (x) + cos (x) = \frac{1}{2}

6 sin^{2} (x) + 9 sin (x) + 3 = 0

cos^{2} (x) + 2 cos (x) - 1 = 0

tan (θ) = 0.1

What is the general solution for 2sin^2(x)+7sin(x)=4 ?
The general solution for 2sin^2(x)+7sin(x)=4 is x= pi/6+2pin,x=(5pi)/6+2pin