What is the general solution for 9cos^2(θ)=-10cos(θ)-1 ?

The general solution for 9cos^2(θ)=-10cos(θ)-1 is θ=1.68213…+2pin,θ=-1.68213…+2pin,θ=pi+2pin

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9cos^2(θ)=-10cos(θ)-1

9 cos^{2} (θ) = - 10 cos (θ) - 1

θ = 1.68213 \dots + 2 πn, θ = - 1.68213 \dots + 2 πn, θ = π + 2 πn

Solution steps

9 cos^{2} (θ) = - 10 cos (θ) - 1

Solve by substitution

cos (θ) = - \frac{1}{9}, cos (θ) = - 1

cos (θ) = - \frac{1}{9} : θ = arccos (- \frac{1}{9}) + 2 πn, θ = - arccos (- \frac{1}{9}) + 2 πn

cos (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

θ = arccos (- \frac{1}{9}) + 2 πn, θ = - arccos (- \frac{1}{9}) + 2 πn, θ = π + 2 πn

Show solutions in decimal form

θ = 1.68213 \dots + 2 πn, θ = - 1.68213 \dots + 2 πn, θ = π + 2 πn

3 sin (x) = 3 sin (2 x)

sin (x) + cos (2 x) = 0.75

sin (x) = 5 sin (x) + 2

2 sin^{2} (x) + (3 - 4) sin (x) = 23

4 cos (30 x) + 12 = 10.5

What is the general solution for 9cos^2(θ)=-10cos(θ)-1 ?
The general solution for 9cos^2(θ)=-10cos(θ)-1 is θ=1.68213…+2pin,θ=-1.68213…+2pin,θ=pi+2pin