What is the general solution for 4cos^2(θ)+3cos(θ)=1 ?

The general solution for 4cos^2(θ)+3cos(θ)=1 is θ=1.31811…+2pin,θ=2pi-1.31811…+2pin,θ=pi+2pin

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4cos^2(θ)+3cos(θ)=1

4 cos^{2} (θ) + 3 cos (θ) = 1

θ = 1.31811 \dots + 2 πn, θ = 2 π - 1.31811 \dots + 2 πn, θ = π + 2 πn

Solution steps

4 cos^{2} (θ) + 3 cos (θ) = 1

Solve by substitution

cos (θ) = \frac{1}{4}, cos (θ) = - 1

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

cos (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

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

Show solutions in decimal form

θ = 1.31811 \dots + 2 πn, θ = 2 π - 1.31811 \dots + 2 πn, θ = π + 2 πn

x, 2 sin^{2} (x) + cos (x) = 1

cos^{2} (x) - 1 = 1 - 2 sin^{2} (x)

400 = 812.25 + 400 - 1140 cos (a)

3 cos (θ) = sin (θ)

- 4 cos^{(2)} (x) + 42 sin (x) + 6 = 0

What is the general solution for 4cos^2(θ)+3cos(θ)=1 ?
The general solution for 4cos^2(θ)+3cos(θ)=1 is θ=1.31811…+2pin,θ=2pi-1.31811…+2pin,θ=pi+2pin