What is the general solution for 3cos^2(θ)+7cos(θ)-9=-3 ?

The general solution for 3cos^2(θ)+7cos(θ)-9=-3 is θ=0.84106…+2pin,θ=2pi-0.84106…+2pin

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3cos^2(θ)+7cos(θ)-9=-3

3 cos^{2} (θ) + 7 cos (θ) - 9 = - 3

θ = 0.84106 \dots + 2 πn, θ = 2 π - 0.84106 \dots + 2 πn

Solution steps

3 cos^{2} (θ) + 7 cos (θ) - 9 = - 3

Solve by substitution

cos (θ) = \frac{2}{3}, cos (θ) = - 3

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

cos (θ) = - 3 :

No Solution

Combine all the solutions

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

Show solutions in decimal form

θ = 0.84106 \dots + 2 πn, θ = 2 π - 0.84106 \dots + 2 πn

1 = 2 sin (x)

\frac{cos ( x )}{sin ( x )} = cos^{2} (x)

sin (2 x - \frac{π}{4}) = 0

7 sin^{2} (θ) - 4 sin (θ) = 3

tan (θ) - cot (θ) = 0

What is the general solution for 3cos^2(θ)+7cos(θ)-9=-3 ?
The general solution for 3cos^2(θ)+7cos(θ)-9=-3 is θ=0.84106…+2pin,θ=2pi-0.84106…+2pin