What is the general solution for 3sin^2(x)+2sin(x)-1=0 ?

The general solution for 3sin^2(x)+2sin(x)-1=0 is x=0.33983…+2pin,x=pi-0.33983…+2pin,x=(3pi)/2+2pin

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3sin^2(x)+2sin(x)-1=0

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

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

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

Solve by substitution

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

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

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

Combine all the solutions

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn, x = \frac{3 π}{2} + 2 πn

Show solutions in decimal form

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn, x = \frac{3 π}{2} + 2 πn

2 cos (θ) = 3

- 73 tan (θ) + 2 = 9

tan^{2} (x) + 2 sec (x) = - 1

2 cos^{2} (θ) + 3 cos (θ) + 1 = 0

tan^{2} (x) sin (x) = - sin (x)

What is the general solution for 3sin^2(x)+2sin(x)-1=0 ?
The general solution for 3sin^2(x)+2sin(x)-1=0 is x=0.33983…+2pin,x=pi-0.33983…+2pin,x=(3pi)/2+2pin