What is the general solution for 4.45tan^2(θ)-23tan(θ)+16.15=0 ?

The general solution for 4.45tan^2(θ)-23tan(θ)+16.15=0 is θ=1.34385…+pin,θ=0.69752…+pin

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4.45tan^2(θ)-23tan(θ)+16.15=0

4.45 tan^{2} (θ) - 23 tan (θ) + 16.15 = 0

θ = 1.34385 \dots + πn, θ = 0.69752 \dots + πn

Solution steps

4.45 tan^{2} (θ) - 23 tan (θ) + 16.15 = 0

Solve by substitution

tan (θ) = \frac{230 + 24153}{89}, tan (θ) = \frac{230 - 24153}{89}

tan (θ) = \frac{230 + 24153}{89} : θ = arctan (\frac{230 + 24153}{89}) + πn

tan (θ) = \frac{230 - 24153}{89} : θ = arctan (\frac{230 - 24153}{89}) + πn

Combine all the solutions

θ = arctan (\frac{230 + 24153}{89}) + πn, θ = arctan (\frac{230 - 24153}{89}) + πn

Show solutions in decimal form

θ = 1.34385 \dots + πn, θ = 0.69752 \dots + πn

sin^{2} (x) = \frac{( 3 m - 2 )}{8}

arccos (x) = arcsin (\frac{1}{3}) + arccos (\frac{1}{4})

sin (2 x) = cos (4 0^{\circ})

- 15 sin (x) - 8 cos (x) = 10

- 5 sec^{2} (x) + 20 = 0

What is the general solution for 4.45tan^2(θ)-23tan(θ)+16.15=0 ?
The general solution for 4.45tan^2(θ)-23tan(θ)+16.15=0 is θ=1.34385…+pin,θ=0.69752…+pin