What is the general solution for tan^2(θ)+7tan(θ)+9=0 ?

The general solution for tan^2(θ)+7tan(θ)+9=0 is θ=-1.03835…+pin,θ=-1.38440…+pin

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tan^2(θ)+7tan(θ)+9=0

tan^{2} (θ) + 7 tan (θ) + 9 = 0

θ = - 1.03835 \dots + πn, θ = - 1.38440 \dots + πn

Solution steps

tan^{2} (θ) + 7 tan (θ) + 9 = 0

Solve by substitution

tan (θ) = \frac{- 7 + 13}{2}, tan (θ) = \frac{- 7 - 13}{2}

tan (θ) = \frac{- 7 + 13}{2} : θ = arctan (\frac{- 7 + 13}{2}) + πn

tan (θ) = \frac{- 7 - 13}{2} : θ = arctan (\frac{- 7 - 13}{2}) + πn

Combine all the solutions

θ = arctan (\frac{- 7 + 13}{2}) + πn, θ = arctan (\frac{- 7 - 13}{2}) + πn

Show solutions in decimal form

θ = - 1.03835 \dots + πn, θ = - 1.38440 \dots + πn

x, cos (x) \cdot cos (y) = 0

3 sec (θ) = 6

cot (x) = csc (x) + 3

cos (x) \cdot cos (3 5^{\circ}) = 1 - sin (x) \cdot sin (3 5^{\circ})

sin (3 θ - 15) = 0.7

What is the general solution for tan^2(θ)+7tan(θ)+9=0 ?
The general solution for tan^2(θ)+7tan(θ)+9=0 is θ=-1.03835…+pin,θ=-1.38440…+pin