What is the general solution for -8=-4+4tan(θ) ?

The general solution for -8=-4+4tan(θ) is θ=(3pi)/4+pin

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-8=-4+4tan(θ)

- 8 = - 4 + 4 tan (θ)

θ = \frac{3 π}{4} + πn

Degrees

θ = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

- 8 = - 4 + 4 tan (θ)

Switch sides

- 4 + 4 tan (θ) = - 8

Move

4

to the right side

- 4 + 4 tan (θ) = - 8

Add

4

to both sides

- 4 + 4 tan (θ) + 4 = - 8 + 4

Simplify

4 tan (θ) = - 4

4 tan (θ) = - 4

Divide both sides by

4

4 tan (θ) = - 4

Divide both sides by

4

\frac{4 tan ( θ )}{4} = \frac{- 4}{4}

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

cos (x) = 0.2588

2 tan^{2} (x) + 3 tan (x) + 1 = 0

- arctan (t) = \frac{4 - π}{4}

cos^{2} (x + 3 0^{\circ}) = \frac{1}{4}

cos (5 7^{\circ}) = sin (x)

What is the general solution for -8=-4+4tan(θ) ?
The general solution for -8=-4+4tan(θ) is θ=(3pi)/4+pin