What is the general solution for tan(2θ)=-sqrt(3),0<= θ<= 360 ?

The general solution for tan(2θ)=-sqrt(3),0<= θ<= 360 is θ=60,θ=150,θ=240,θ=330

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tan(2θ)=-sqrt(3),0<= θ<= 360

tan (2 θ) = - 3, 0^{\circ} \leq θ \leq 36 0^{\circ}

θ = 6 0^{\circ}, θ = 15 0^{\circ}, θ = 24 0^{\circ}, θ = 33 0^{\circ}

Radians

θ = \frac{π}{3}, θ = \frac{5 π}{6}, θ = \frac{4 π}{3}, θ = \frac{11 π}{6}

Solution steps

tan (2 θ) = - 3, 0^{\circ} \leq θ \leq 36 0^{\circ}

General solutions for

tan (2 θ) = - 3

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

2 θ = 12 0^{\circ} + 18 0^{\circ} n

2 θ = 12 0^{\circ} + 18 0^{\circ} n

Solve

2 θ = 12 0^{\circ} + 18 0^{\circ} n : θ = 6 0^{\circ} + \frac{18 0 ^{\circ} n}{2}

2 θ = 12 0^{\circ} + 18 0^{\circ} n

Divide both sides by

2

2 θ = 12 0^{\circ} + 18 0^{\circ} n

Divide both sides by

2

\frac{2 θ}{2} = \frac{12 0 ^{\circ}}{2} + \frac{18 0 ^{\circ} n}{2}

Simplify

\frac{2 θ}{2} = \frac{12 0 ^{\circ}}{2} + \frac{18 0 ^{\circ} n}{2}

Simplify

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Divide the numbers:

\frac{2}{2} = 1

= θ

Simplify

\frac{12 0 ^{\circ}}{2} + \frac{18 0 ^{\circ} n}{2} : 6 0^{\circ} + \frac{18 0 ^{\circ} n}{2}

\frac{12 0 ^{\circ}}{2} + \frac{18 0 ^{\circ} n}{2}

\frac{12 0 ^{\circ}}{2} = 6 0^{\circ}

\frac{12 0 ^{\circ}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{36 0 ^{\circ}}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= 6 0^{\circ}

Cancel the common factor:

2

= 6 0^{\circ}

= 6 0^{\circ} + \frac{18 0 ^{\circ} n}{2}

θ = 6 0^{\circ} + \frac{18 0 ^{\circ} n}{2}

θ = 6 0^{\circ} + \frac{18 0 ^{\circ} n}{2}

θ = 6 0^{\circ} + \frac{18 0 ^{\circ} n}{2}

θ = 6 0^{\circ} + \frac{18 0 ^{\circ} n}{2}

Solutions for the range

0 \leq θ \leq 36 0^{\circ}

θ = 6 0^{\circ}, θ = 15 0^{\circ}, θ = 24 0^{\circ}, θ = 33 0^{\circ}

0 = tan (c)

cos (t) - cos (2 t) = 0

4 sin (θ) = - 2 cos (θ)

cot (2 x) = - 1, (0, 2 π)

(sin (x) + 2) (tan (x) - 2) = 0

What is the general solution for tan(2θ)=-sqrt(3),0<= θ<= 360 ?
The general solution for tan(2θ)=-sqrt(3),0<= θ<= 360 is θ=60,θ=150,θ=240,θ=330