What is the general solution for 3tan(x/2)+3=0 ?

The general solution for 3tan(x/2)+3=0 is x=(3pi)/2+2pin

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Popular >

3tan(x/2)+3=0

Solution

3 tan (\frac{x}{2}) + 3 = 0

Solution

x = \frac{3 π}{2} + 2 πn

Degrees

x = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

3 tan (\frac{x}{2}) + 3 = 0

Move

3

to the right side

3 tan (\frac{x}{2}) + 3 = 0

Subtract

3

from both sides

3 tan (\frac{x}{2}) + 3 - 3 = 0 - 3

Simplify

3 tan (\frac{x}{2}) = - 3

3 tan (\frac{x}{2}) = - 3

Divide both sides by

3

3 tan (\frac{x}{2}) = - 3

Divide both sides by

3

\frac{3 tan ( \frac{x}{2} )}{3} = \frac{- 3}{3}

Simplify

tan (\frac{x}{2}) = - 1

tan (\frac{x}{2}) = - 1

General solutions for

tan (\frac{x}{2}) = - 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}

\frac{x}{2} = \frac{3 π}{4} + πn

\frac{x}{2} = \frac{3 π}{4} + πn

Solve

\frac{x}{2} = \frac{3 π}{4} + πn : x = \frac{3 π}{2} + 2 πn

\frac{x}{2} = \frac{3 π}{4} + πn

Multiply both sides by

2

\frac{x}{2} = \frac{3 π}{4} + πn

Multiply both sides by

2

\frac{2 x}{2} = 2 \cdot \frac{3 π}{4} + 2 πn

Simplify

\frac{2 x}{2} = 2 \cdot \frac{3 π}{4} + 2 πn

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

2 \cdot \frac{3 π}{4} + 2 πn : \frac{3 π}{2} + 2 πn

2 \cdot \frac{3 π}{4} + 2 πn

2 \cdot \frac{3 π}{4} = \frac{3 π}{2}

2 \cdot \frac{3 π}{4}

Multiply fractions:

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

= \frac{3 π 2}{4}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{6 π}{4}

Cancel the common factor:

2

= \frac{3 π}{2}

= \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

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Frequently Asked Questions (FAQ)

What is the general solution for 3tan(x/2)+3=0 ?
The general solution for 3tan(x/2)+3=0 is x=(3pi)/2+2pin