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

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

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tan(θ)= 4/(-4)

tan (θ) = \frac{4}{- 4}

θ = \frac{3 π}{4} + πn

Solution steps

tan (θ) = \frac{4}{- 4}

Simplify

\frac{4}{- 4} : - 1

\frac{4}{- 4}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{4}{4}

Apply rule

\frac{a}{a} = 1

= - 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

sin (x) = \frac{2}{7}

sin (θ) cos (θ) + sin (θ) = 0

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

45.6 = arcsin (\frac{n ^{1}}{n ^{2}}), n^{1}

tan (x) = 0.839

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