What is the general solution for tan(θ)+sqrt(3)=0 ?

The general solution for tan(θ)+sqrt(3)=0 is θ=(2pi)/3+pin

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tan(θ)+sqrt(3)=0

tan (θ) + 3 = 0

θ = \frac{2 π}{3} + πn

Degrees

θ = 12 0^{\circ} + 18 0^{\circ} n

Solution steps

tan (θ) + 3 = 0

Move

3

to the right side

tan (θ) + 3 = 0

Subtract

3

from both sides

tan (θ) + 3 - 3 = 0 - 3

Simplify

tan (θ) = - 3

tan (θ) = - 3

General solutions for

tan (θ) = - 3

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

θ = \frac{2 π}{3} + πn

θ = \frac{2 π}{3} + πn

csc (\frac{π}{2})

2 cos (x) = 3

csc (3 0^{\circ})

2 sin^{2} (x) + sin (x) - 1 = 0

cos (- 105 0^{\circ})

What is the general solution for tan(θ)+sqrt(3)=0 ?
The general solution for tan(θ)+sqrt(3)=0 is θ=(2pi)/3+pin