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

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

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4tan^2(θ)-9=0

4 tan^{2} (θ) - 9 = 0

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

Solution steps

4 tan^{2} (θ) - 9 = 0

Solve by substitution

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

tan (θ) = \frac{3}{2} : θ = arctan (\frac{3}{2}) + πn

tan (θ) = - \frac{3}{2} : θ = arctan (- \frac{3}{2}) + πn

Combine all the solutions

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

Show solutions in decimal form

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

sin (θ) = 7.19

3 = \frac{π}{3} sec^{2} (c)

\frac{sin ( 9 0 ^{\circ} )}{3.37} = \frac{sin ( x )}{0.7}

cos (x) = \frac{1 - cos ( x )}{2}

7 cos (4 x) = 6

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