What is the general solution for tan(θ)=(-4sqrt(3))/4 ?

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

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tan(θ)=(-4sqrt(3))/4

tan (θ) = \frac{- 4 3}{4}

θ = \frac{2 π}{3} + πn

Solution steps

tan (θ) = \frac{- 4 3}{4}

Simplify

\frac{- 4 3}{4} : - 3

\frac{- 4 3}{4}

Apply the fraction rule:

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

= - \frac{4 3}{4}

Divide the numbers:

\frac{4}{4} = 1

= - 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

3 sin (x) - cos (x) = 3, 0 \leq x \leq 2 π

- 1 + 3 sin (x) = - 1 + 4 sin (x)

cos (x) = \frac{6}{25}

3 sin (φ) - cos (2 φ) = 1

cos (4 x) = 2 cos (2 x) - 1

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