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

The general solution for 2tan(θ)+2=0 is θ=(3pi)/4+pin

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2tan(θ)+2=0

2 tan (θ) + 2 = 0

θ = \frac{3 π}{4} + πn

Degrees

θ = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

2 tan (θ) + 2 = 0

Move

2

to the right side

2 tan (θ) + 2 = 0

Subtract

2

from both sides

2 tan (θ) + 2 - 2 = 0 - 2

Simplify

2 tan (θ) = - 2

2 tan (θ) = - 2

Divide both sides by

2

2 tan (θ) = - 2

Divide both sides by

2

\frac{2 tan ( θ )}{2} = \frac{- 2}{2}

Simplify

tan (θ) = - 1

tan (θ) = - 1

General solutions for

tan (θ) = - 1

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{3 π}{4} + πn

θ = \frac{3 π}{4} + πn

8 cos (θ) + 43 = 0

cot (x) (tan (x) + \frac{3}{3}) = 0

cos^{2} (x) - \frac{1}{2} cos (x) = 0

7 sec (x) - 7 = 0

sin (θ) = 0.48

What is the general solution for 2tan(θ)+2=0 ?
The general solution for 2tan(θ)+2=0 is θ=(3pi)/4+pin