What is the general solution for 6cos^2(θ)+7=-17cos(θ) ?

The general solution for 6cos^2(θ)+7=-17cos(θ) is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin

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6cos^2(θ)+7=-17cos(θ)

6 cos^{2} (θ) + 7 = - 17 cos (θ)

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

Solution steps

6 cos^{2} (θ) + 7 = - 17 cos (θ)

Solve by substitution

cos (θ) = - \frac{1}{2}, cos (θ) = - \frac{7}{3}

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

cos (θ) = - \frac{7}{3} :

No Solution

Combine all the solutions

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

0 = - 9 \cdot sin (2 x)

sec^{2} (x) = 4 tan^{2} (x)

5 sin (x) = - 4

- π sin (π x) = 0

7 tan (4 x + 199) = 8 sin (4 x + 199)

What is the general solution for 6cos^2(θ)+7=-17cos(θ) ?
The general solution for 6cos^2(θ)+7=-17cos(θ) is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin