What is the general solution for -4tan^2(θ)-9tan(θ)-2=0 ?

The general solution for -4tan^2(θ)-9tan(θ)-2=0 is θ=-1.10714…+pin,θ=-0.24497…+pin

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-4tan^2(θ)-9tan(θ)-2=0

- 4 tan^{2} (θ) - 9 tan (θ) - 2 = 0

θ = - 1.10714 \dots + πn, θ = - 0.24497 \dots + πn

Solution steps

- 4 tan^{2} (θ) - 9 tan (θ) - 2 = 0

Solve by substitution

tan (θ) = - 2, tan (θ) = - \frac{1}{4}

tan (θ) = - 2 : θ = arctan (- 2) + πn

tan (θ) = - \frac{1}{4} : θ = arctan (- \frac{1}{4}) + πn

Combine all the solutions

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

Show solutions in decimal form

θ = - 1.10714 \dots + πn, θ = - 0.24497 \dots + πn

3 cos (θ) - 2 = 0

csc^{2} (\frac{x}{2}) + csc (\frac{x}{2}) = 4 + 4 sin (\frac{x}{2})

(cot (x) - 1) (sin (x) + 1) = 0

3 cos (x) = sin (x) + 1

4 tan^{3} (x) - 12 tan (x) = 0

What is the general solution for -4tan^2(θ)-9tan(θ)-2=0 ?
The general solution for -4tan^2(θ)-9tan(θ)-2=0 is θ=-1.10714…+pin,θ=-0.24497…+pin