What is the general solution for 3tan(θ)=-3,0<= θ<= 2pi ?

The general solution for 3tan(θ)=-3,0<= θ<= 2pi is θ=(3pi)/4 ,θ=(7pi)/4

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3tan(θ)=-3,0<= θ<= 2pi

3 tan (θ) = - 3, 0 \leq θ \leq 2 π

θ = \frac{3 π}{4}, θ = \frac{7 π}{4}

Degrees

θ = 13 5^{\circ}, θ = 31 5^{\circ}

Solution steps

3 tan (θ) = - 3, 0 \leq θ \leq 2 π

Divide both sides by

3

3 tan (θ) = - 3

Divide both sides by

3

\frac{3 tan ( θ )}{3} = \frac{- 3}{3}

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

Solutions for the range

0 \leq θ \leq 2 π

θ = \frac{3 π}{4}, θ = \frac{7 π}{4}

sin (x) = \frac{39}{62}

2 cot^{2} (x) - csc^{2} (x) + csc (x) = 4

2 \cdot sin (x) + 1 = 3 \cdot cos (x)

\frac{sin ( θ )}{cos ( θ )} = 0

0 = sin (y)

What is the general solution for 3tan(θ)=-3,0<= θ<= 2pi ?
The general solution for 3tan(θ)=-3,0<= θ<= 2pi is θ=(3pi)/4 ,θ=(7pi)/4