What is the general solution for 7sin^2(θ)-36sin(θ)+5=0 ?

The general solution for 7sin^2(θ)-36sin(θ)+5=0 is θ=0.14334…+2pin,θ=pi-0.14334…+2pin

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7sin^2(θ)-36sin(θ)+5=0

7 sin^{2} (θ) - 36 sin (θ) + 5 = 0

θ = 0.14334 \dots + 2 πn, θ = π - 0.14334 \dots + 2 πn

Solution steps

7 sin^{2} (θ) - 36 sin (θ) + 5 = 0

Solve by substitution

sin (θ) = 5, sin (θ) = \frac{1}{7}

sin (θ) = 5 :

No Solution

sin (θ) = \frac{1}{7} : θ = arcsin (\frac{1}{7}) + 2 πn, θ = π - arcsin (\frac{1}{7}) + 2 πn

Combine all the solutions

θ = arcsin (\frac{1}{7}) + 2 πn, θ = π - arcsin (\frac{1}{7}) + 2 πn

Show solutions in decimal form

θ = 0.14334 \dots + 2 πn, θ = π - 0.14334 \dots + 2 πn

cos (x) = 1 - sin^{2} (x)

tan (\frac{2 x}{3}) = 0

3 cos^{2} (A) + 3 cos (A) = 0

3 csc (2 x) - 2 = 0

cos (3 x) (2 cos (x) + 1) = 0

What is the general solution for 7sin^2(θ)-36sin(θ)+5=0 ?
The general solution for 7sin^2(θ)-36sin(θ)+5=0 is θ=0.14334…+2pin,θ=pi-0.14334…+2pin