What is the general solution for 8.59tan^2(θ)-24tan(θ)+15.29=0 ?

The general solution for 8.59tan^2(θ)-24tan(θ)+15.29=0 is θ=1.06631…+pin,θ=0.77671…+pin

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8.59tan^2(θ)-24tan(θ)+15.29=0

8.59 tan^{2} (θ) - 24 tan (θ) + 15.29 = 0

θ = 1.06631 \dots + πn, θ = 0.77671 \dots + πn

Solution steps

8.59 tan^{2} (θ) - 24 tan (θ) + 15.29 = 0

Solve by substitution

tan (θ) = \frac{1200 + 126589}{859}, tan (θ) = \frac{1200 - 126589}{859}

tan (θ) = \frac{1200 + 126589}{859} : θ = arctan (\frac{1200 + 126589}{859}) + πn

tan (θ) = \frac{1200 - 126589}{859} : θ = arctan (\frac{1200 - 126589}{859}) + πn

Combine all the solutions

θ = arctan (\frac{1200 + 126589}{859}) + πn, θ = arctan (\frac{1200 - 126589}{859}) + πn

Show solutions in decimal form

θ = 1.06631 \dots + πn, θ = 0.77671 \dots + πn

(csc (x)) = - csc (x) cot (x)

cot (x) = - \frac{4}{3}

\frac{cos ^{2} ( x )}{sin ^{2} ( x )} = 1

x, f = \frac{cos ( 2 x )}{cos ( x ) - sin ( x )}

cos (2 x) + 5 = 6.25

What is the general solution for 8.59tan^2(θ)-24tan(θ)+15.29=0 ?
The general solution for 8.59tan^2(θ)-24tan(θ)+15.29=0 is θ=1.06631…+pin,θ=0.77671…+pin