What is the general solution for -3sin^2(θ)+4sin(θ)-7=-6 ?

The general solution for -3sin^2(θ)+4sin(θ)-7=-6 is θ=0.33983…+2pin,θ=pi-0.33983…+2pin,θ= pi/2+2pin

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-3sin^2(θ)+4sin(θ)-7=-6

- 3 sin^{2} (θ) + 4 sin (θ) - 7 = - 6

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

Solution steps

- 3 sin^{2} (θ) + 4 sin (θ) - 7 = - 6

Solve by substitution

sin (θ) = \frac{1}{3}, sin (θ) = 1

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

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

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

Show solutions in decimal form

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

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

sin (x + \frac{π}{6}) + cos (x + \frac{π}{6}) = 1

sin (x) = - 1, 0 \leq x \leq 2 π

- 3 sin (x) + cos (x) = 0

2 sin^{2} (x) + 5 cos (x) - 4 = 0

What is the general solution for -3sin^2(θ)+4sin(θ)-7=-6 ?
The general solution for -3sin^2(θ)+4sin(θ)-7=-6 is θ=0.33983…+2pin,θ=pi-0.33983…+2pin,θ= pi/2+2pin