What is the general solution for 3sin^2(θ)-7sin(θ)+2=0 ?

The general solution for 3sin^2(θ)-7sin(θ)+2=0 is θ=0.33983…+2pin,θ=pi-0.33983…+2pin

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3sin^2(θ)-7sin(θ)+2=0

3 sin^{2} (θ) - 7 sin (θ) + 2 = 0

θ = 0.33983 \dots + 2 πn, θ = π - 0.33983 \dots + 2 πn

Solution steps

3 sin^{2} (θ) - 7 sin (θ) + 2 = 0

Solve by substitution

sin (θ) = 2, sin (θ) = \frac{1}{3}

sin (θ) = 2 :

No Solution

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

Combine all the solutions

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

Show solutions in decimal form

θ = 0.33983 \dots + 2 πn, θ = π - 0.33983 \dots + 2 πn

9 sin^{2} (θ) + 14 cos (θ) - 12 = 5 cos (θ) - 1

4 sec^{2} (x) - 2 = 0

cos (x) = \frac{1}{3}

sin (x) cos (x) = \frac{3}{4}, 0 \leq x \leq 2 π

2 cos^{2} (x) + sin (x) - 1 = 0, 0 \leq x < 2 π

What is the general solution for 3sin^2(θ)-7sin(θ)+2=0 ?
The general solution for 3sin^2(θ)-7sin(θ)+2=0 is θ=0.33983…+2pin,θ=pi-0.33983…+2pin