What is the general solution for sqrt(3)tan(3x)+sqrt(3)=0,0<= x<= 180 ?

Q: What is the general solution for sqrt(3)tan(3x)+sqrt(3)=0,0<= x<= 180 ?

The general solution for sqrt(3)tan(3x)+sqrt(3)=0,0<= x<= 180 is x=45,x=105,x=165

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Popular Trigonometry >

sqrt(3)tan(3x)+sqrt(3)=0,0<= x<= 180

Solution

3 tan (3 x) + 3 = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

Solution

x = 4 5^{\circ}, x = 10 5^{\circ}, x = 16 5^{\circ}

Radians

x = \frac{π}{4}, x = \frac{7 π}{12}, x = \frac{11 π}{12}

Solution steps

3 tan (3 x) + 3 = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

Move

3

to the right side

3 tan (3 x) + 3 = 0

Subtract

3

from both sides

3 tan (3 x) + 3 - 3 = 0 - 3

Simplify

3 tan (3 x) = - 3

3 tan (3 x) = - 3

Divide both sides by

3

3 tan (3 x) = - 3

Divide both sides by

3

\frac{3 tan ( 3 x )}{3} = \frac{- 3}{3}

Simplify

tan (3 x) = - 1

tan (3 x) = - 1

General solutions for

tan (3 x) = - 1

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}

3 x = 13 5^{\circ} + 18 0^{\circ} n

3 x = 13 5^{\circ} + 18 0^{\circ} n

Solve

3 x = 13 5^{\circ} + 18 0^{\circ} n : x = 4 5^{\circ} + \frac{18 0 ^{\circ} n}{3}

3 x = 13 5^{\circ} + 18 0^{\circ} n

Divide both sides by

3

3 x = 13 5^{\circ} + 18 0^{\circ} n

Divide both sides by

3

\frac{3 x}{3} = \frac{13 5 ^{\circ}}{3} + \frac{18 0 ^{\circ} n}{3}

Simplify

\frac{3 x}{3} = \frac{13 5 ^{\circ}}{3} + \frac{18 0 ^{\circ} n}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{13 5 ^{\circ}}{3} + \frac{18 0 ^{\circ} n}{3} : 4 5^{\circ} + \frac{18 0 ^{\circ} n}{3}

\frac{13 5 ^{\circ}}{3} + \frac{18 0 ^{\circ} n}{3}

\frac{13 5 ^{\circ}}{3} = 4 5^{\circ}

\frac{13 5 ^{\circ}}{3}

Apply the fraction rule:

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

= \frac{54 0 ^{\circ}}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= 4 5^{\circ}

Cancel the common factor:

3

= 4 5^{\circ}

= 4 5^{\circ} + \frac{18 0 ^{\circ} n}{3}

x = 4 5^{\circ} + \frac{18 0 ^{\circ} n}{3}

x = 4 5^{\circ} + \frac{18 0 ^{\circ} n}{3}

x = 4 5^{\circ} + \frac{18 0 ^{\circ} n}{3}

x = 4 5^{\circ} + \frac{18 0 ^{\circ} n}{3}

Solutions for the range

0 \leq x \leq 18 0^{\circ}

x = 4 5^{\circ}, x = 10 5^{\circ}, x = 16 5^{\circ}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for sqrt(3)tan(3x)+sqrt(3)=0,0<= x<= 180 ?
The general solution for sqrt(3)tan(3x)+sqrt(3)=0,0<= x<= 180 is x=45,x=105,x=165