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

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

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tan(θ)=(-3)/3

tan (θ) = \frac{- 3}{3}

θ = \frac{3 π}{4} + πn

Solution steps

tan (θ) = \frac{- 3}{3}

Simplify

\frac{- 3}{3} : - 1

\frac{- 3}{3}

Apply the fraction rule:

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

= - \frac{3}{3}

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

csc (2 θ) = \frac{1}{2} (sec (θ)) (cos (θ))

sec^{2} (x) + 2 sec (x) - 8 = 0

3 cos^{2} (x) + 4 sin (x) - 4 = 0

sin (x) = \frac{7}{15}

3 sec (x) = 9

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