What is the general solution for 7cos^2(θ)+11cos(θ)=cos(θ)-3 ?

The general solution for 7cos^2(θ)+11cos(θ)=cos(θ)-3 is θ=2.01370…+2pin,θ=-2.01370…+2pin,θ=pi+2pin

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7cos^2(θ)+11cos(θ)=cos(θ)-3

7 cos^{2} (θ) + 11 cos (θ) = cos (θ) - 3

θ = 2.01370 \dots + 2 πn, θ = - 2.01370 \dots + 2 πn, θ = π + 2 πn

Solution steps

7 cos^{2} (θ) + 11 cos (θ) = cos (θ) - 3

Solve by substitution

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

cos (θ) = - \frac{3}{7} : θ = arccos (- \frac{3}{7}) + 2 πn, θ = - arccos (- \frac{3}{7}) + 2 πn

cos (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

θ = arccos (- \frac{3}{7}) + 2 πn, θ = - arccos (- \frac{3}{7}) + 2 πn, θ = π + 2 πn

Show solutions in decimal form

θ = 2.01370 \dots + 2 πn, θ = - 2.01370 \dots + 2 πn, θ = π + 2 πn

cos^{2} (x) - 9 cos (x) - 1 = 0

3 tan (x) = 2 sin (x)

12 arcsin (x) = 4 π

sec (x) = 2, 0 \leq x \leq 2 π

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

What is the general solution for 7cos^2(θ)+11cos(θ)=cos(θ)-3 ?
The general solution for 7cos^2(θ)+11cos(θ)=cos(θ)-3 is θ=2.01370…+2pin,θ=-2.01370…+2pin,θ=pi+2pin