What is the general solution for -4cos^2(θ)-11cos(θ)-1=-7cos(θ) ?

The general solution for -4cos^2(θ)-11cos(θ)-1=-7cos(θ) is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin

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-4cos^2(θ)-11cos(θ)-1=-7cos(θ)

- 4 cos^{2} (θ) - 11 cos (θ) - 1 = - 7 cos (θ)

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

Solution steps

- 4 cos^{2} (θ) - 11 cos (θ) - 1 = - 7 cos (θ)

Solve by substitution

cos (θ) = - \frac{1}{2}

cos (θ) = - \frac{1}{2} : θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

Combine all the solutions

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

0 = 1 + cos (\frac{x}{2})

sin (x) = cos (1 9^{\circ})

\frac{1}{1.5} = \frac{sin ( 3 0 ^{\circ} )}{sin ( x )}, x < 9 0^{\circ}

tan (A) = \frac{8}{15}

tan^{2} (θ) = sec^{2} (θ) + 1

What is the general solution for -4cos^2(θ)-11cos(θ)-1=-7cos(θ) ?
The general solution for -4cos^2(θ)-11cos(θ)-1=-7cos(θ) is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin