What is the general solution for 4sin^2(θ)-sin(θ)-4=0 ?

The general solution for 4sin^2(θ)-sin(θ)-4=0 is θ=-1.08175…+2pin,θ=pi+1.08175…+2pin

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4sin^2(θ)-sin(θ)-4=0

4 sin^{2} (θ) - sin (θ) - 4 = 0

θ = - 1.08175 \dots + 2 πn, θ = π + 1.08175 \dots + 2 πn

Solution steps

4 sin^{2} (θ) - sin (θ) - 4 = 0

Solve by substitution

sin (θ) = \frac{1 + 65}{8}, sin (θ) = \frac{1 - 65}{8}

sin (θ) = \frac{1 + 65}{8} :

No Solution

sin (θ) = \frac{1 - 65}{8} : θ = arcsin (\frac{1 - 65}{8}) + 2 πn, θ = π + arcsin (- \frac{1 - 65}{8}) + 2 πn

Combine all the solutions

θ = arcsin (\frac{1 - 65}{8}) + 2 πn, θ = π + arcsin (- \frac{1 - 65}{8}) + 2 πn

Show solutions in decimal form

θ = - 1.08175 \dots + 2 πn, θ = π + 1.08175 \dots + 2 πn

tan (θ) = 1

sin (2 θ) + cos (2 θ) = 0

5 cot^{2} (x) - 15 = 0

sin (x) = \frac{2}{5}

csc (x) = 5

What is the general solution for 4sin^2(θ)-sin(θ)-4=0 ?
The general solution for 4sin^2(θ)-sin(θ)-4=0 is θ=-1.08175…+2pin,θ=pi+1.08175…+2pin