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

The general solution for 9cot^2(θ)-4=0 is θ=0.98279…+pin,θ=2.15879…+pin

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9cot^2(θ)-4=0

9 cot^{2} (θ) - 4 = 0

θ = 0.98279 \dots + πn, θ = 2.15879 \dots + πn

Solution steps

9 cot^{2} (θ) - 4 = 0

Solve by substitution

cot (θ) = \frac{2}{3}, cot (θ) = - \frac{2}{3}

cot (θ) = \frac{2}{3} : θ = arccot (\frac{2}{3}) + πn

cot (θ) = - \frac{2}{3} : θ = arccot (- \frac{2}{3}) + πn

Combine all the solutions

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

Show solutions in decimal form

θ = 0.98279 \dots + πn, θ = 2.15879 \dots + πn

4 sin^{2} (θ) = 1 + 4 cos (θ)

4 sin (θ) + 1 = 2 sin (θ)

cot (θ) = \frac{1}{2}

sin (θ) = 0.7

sin (θ) = 0.2

What is the general solution for 9cot^2(θ)-4=0 ?
The general solution for 9cot^2(θ)-4=0 is θ=0.98279…+pin,θ=2.15879…+pin