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

The general solution for 4sin^2(θ)+4cos(θ)=0 is θ=2.23703…+2pin,θ=-2.23703…+2pin

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4sin^2(θ)+4cos(θ)=0

4 sin^{2} (θ) + 4 cos (θ) = 0

θ = 2.23703 \dots + 2 πn, θ = - 2.23703 \dots + 2 πn

Solution steps

4 sin^{2} (θ) + 4 cos (θ) = 0

Rewrite using trig identities

(1 - cos^{2} (θ)) \cdot 4 + 4 cos (θ) = 0

Solve by substitution

cos (θ) = - \frac{- 1 + 5}{2}, cos (θ) = \frac{1 + 5}{2}

cos (θ) = - \frac{- 1 + 5}{2} : θ = arccos (- \frac{- 1 + 5}{2}) + 2 πn, θ = - arccos (- \frac{- 1 + 5}{2}) + 2 πn

cos (θ) = \frac{1 + 5}{2} :

No Solution

Combine all the solutions

θ = arccos (- \frac{- 1 + 5}{2}) + 2 πn, θ = - arccos (- \frac{- 1 + 5}{2}) + 2 πn

Show solutions in decimal form

θ = 2.23703 \dots + 2 πn, θ = - 2.23703 \dots + 2 πn

cos^{2} (x) = \frac{( 8 k - 9 )}{9}

sin (x) + cot (x) cos (x) = 3

4 sin^{4} (x) + 3 sin^{2} (x) - 1 = 0

3 tan (θ) - 3 = 0

cot (θ) = \frac{1}{cot ( θ )}

What is the general solution for 4sin^2(θ)+4cos(θ)=0 ?
The general solution for 4sin^2(θ)+4cos(θ)=0 is θ=2.23703…+2pin,θ=-2.23703…+2pin