What is the general solution for sqrt(3)tan(4x)+1=0 ?

The general solution for sqrt(3)tan(4x)+1=0 is x=(5pi}{24}+\frac{pin)/4

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Popular >

sqrt(3)tan(4x)+1=0

Solution

3 tan (4 x) + 1 = 0

Solution

x = \frac{5 π}{24} + \frac{πn}{4}

Degrees

x = 37. 5^{\circ} + 4 5^{\circ} n

Solution steps

3 tan (4 x) + 1 = 0

Move

1

to the right side

3 tan (4 x) + 1 = 0

Subtract

1

from both sides

3 tan (4 x) + 1 - 1 = 0 - 1

Simplify

3 tan (4 x) = - 1

3 tan (4 x) = - 1

Divide both sides by

3

3 tan (4 x) = - 1

Divide both sides by

3

\frac{3 tan ( 4 x )}{3} = \frac{- 1}{3}

Simplify

\frac{3 tan ( 4 x )}{3} = \frac{- 1}{3}

Simplify

\frac{3 tan ( 4 x )}{3} : tan (4 x)

\frac{3 tan ( 4 x )}{3}

Cancel the common factor:

3

= tan (4 x)

Simplify

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

\frac{- 1}{3}

Apply the fraction rule:

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

= - \frac{1}{3}

Rationalize

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

- \frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= - \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= - \frac{3}{3}

= - \frac{3}{3}

tan (4 x) = - \frac{3}{3}

tan (4 x) = - \frac{3}{3}

tan (4 x) = - \frac{3}{3}

General solutions for

tan (4 x) = - \frac{3}{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}

4 x = \frac{5 π}{6} + πn

4 x = \frac{5 π}{6} + πn

Solve

4 x = \frac{5 π}{6} + πn : x = \frac{5 π}{24} + \frac{πn}{4}

4 x = \frac{5 π}{6} + πn

Divide both sides by

4

4 x = \frac{5 π}{6} + πn

Divide both sides by

4

\frac{4 x}{4} = \frac{\frac{5 π}{6}}{4} + \frac{πn}{4}

Simplify

\frac{4 x}{4} = \frac{\frac{5 π}{6}}{4} + \frac{πn}{4}

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

\frac{\frac{5 π}{6}}{4} + \frac{πn}{4} : \frac{5 π}{24} + \frac{πn}{4}

\frac{\frac{5 π}{6}}{4} + \frac{πn}{4}

\frac{\frac{5 π}{6}}{4} = \frac{5 π}{24}

\frac{\frac{5 π}{6}}{4}

Apply the fraction rule:

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

= \frac{5 π}{6 \cdot 4}

Multiply the numbers:

6 \cdot 4 = 24

= \frac{5 π}{24}

= \frac{5 π}{24} + \frac{πn}{4}

x = \frac{5 π}{24} + \frac{πn}{4}

x = \frac{5 π}{24} + \frac{πn}{4}

x = \frac{5 π}{24} + \frac{πn}{4}

x = \frac{5 π}{24} + \frac{πn}{4}

Graph

Popular Examples

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2sin(x-pi/3)+sqrt(2)=0

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sin^2(θ)+3=2cos^2(θ)+4sin(θ)

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2cos(2x)+3=4cos(x)

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Frequently Asked Questions (FAQ)

What is the general solution for sqrt(3)tan(4x)+1=0 ?
The general solution for sqrt(3)tan(4x)+1=0 is x=(5pi}{24}+\frac{pin)/4