What is the general solution for 3/2 tan(2x+135)=-(sqrt(3))/2 ?

The general solution for 3/2 tan(2x+135)=-(sqrt(3))/2 is x=-135/2+(5pi}{12}+\frac{pin)/2

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Popular Trigonometry >

3/2 tan(2x+135)=-(sqrt(3))/2

Solution

\frac{3}{2} tan (2 x + 135) = - \frac{3}{2}

Solution

x = - \frac{135}{2} + \frac{5 π}{12} + \frac{πn}{2}

Degrees

x = - 3792.46511 \dots^{\circ} + 9 0^{\circ} n

Solution steps

\frac{3}{2} tan (2 x + 135) = - \frac{3}{2}

Multiply both sides by

2

\frac{3}{2} tan (2 x + 135) = - \frac{3}{2}

Multiply both sides by

2

2 \cdot \frac{3}{2} tan (2 x + 135) = 2 (- \frac{3}{2})

Simplify

2 \cdot \frac{3}{2} tan (2 x + 135) = 2 (- \frac{3}{2})

Simplify

2 \cdot \frac{3}{2} tan (2 x + 135) : 3 tan (2 x + 135)

2 \cdot \frac{3}{2} tan (2 x + 135)

Multiply fractions:

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

= \frac{3 \cdot 2}{2} tan (2 x + 135)

Cancel the common factor:

2

= tan (2 x + 135) \cdot 3

Simplify

2 (- \frac{3}{2}) : - 3

2 (- \frac{3}{2})

Remove parentheses:

(- a) = - a

= - 2 \cdot \frac{3}{2}

Multiply fractions:

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

= - \frac{3 \cdot 2}{2}

Cancel the common factor:

2

= - 3

3 tan (2 x + 135) = - 3

3 tan (2 x + 135) = - 3

3 tan (2 x + 135) = - 3

Divide both sides by

3

3 tan (2 x + 135) = - 3

Divide both sides by

3

\frac{3 tan ( 2 x + 135 )}{3} = \frac{- 3}{3}

Simplify

tan (2 x + 135) = - \frac{3}{3}

tan (2 x + 135) = - \frac{3}{3}

General solutions for

tan (2 x + 135) = - \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}

2 x + 135 = \frac{5 π}{6} + πn

2 x + 135 = \frac{5 π}{6} + πn

Solve

2 x + 135 = \frac{5 π}{6} + πn : x = - \frac{135}{2} + \frac{5 π}{12} + \frac{πn}{2}

2 x + 135 = \frac{5 π}{6} + πn

Move

135

to the right side

2 x + 135 = \frac{5 π}{6} + πn

Subtract

135

from both sides

2 x + 135 - 135 = \frac{5 π}{6} + πn - 135

Simplify

2 x = \frac{5 π}{6} + πn - 135

2 x = \frac{5 π}{6} + πn - 135

Divide both sides by

2

2 x = \frac{5 π}{6} + πn - 135

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{5 π}{6}}{2} + \frac{πn}{2} - \frac{135}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{5 π}{6}}{2} + \frac{πn}{2} - \frac{135}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{5 π}{6}}{2} + \frac{πn}{2} - \frac{135}{2} : - \frac{135}{2} + \frac{5 π}{12} + \frac{πn}{2}

\frac{\frac{5 π}{6}}{2} + \frac{πn}{2} - \frac{135}{2}

Group like terms

= - \frac{135}{2} + \frac{πn}{2} + \frac{\frac{5 π}{6}}{2}

\frac{\frac{5 π}{6}}{2} = \frac{5 π}{12}

\frac{\frac{5 π}{6}}{2}

Apply the fraction rule:

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

= \frac{5 π}{6 \cdot 2}

Multiply the numbers:

6 \cdot 2 = 12

= \frac{5 π}{12}

= - \frac{135}{2} + \frac{πn}{2} + \frac{5 π}{12}

Group like terms

= - \frac{135}{2} + \frac{5 π}{12} + \frac{πn}{2}

x = - \frac{135}{2} + \frac{5 π}{12} + \frac{πn}{2}

x = - \frac{135}{2} + \frac{5 π}{12} + \frac{πn}{2}

x = - \frac{135}{2} + \frac{5 π}{12} + \frac{πn}{2}

x = - \frac{135}{2} + \frac{5 π}{12} + \frac{πn}{2}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 3/2 tan(2x+135)=-(sqrt(3))/2 ?
The general solution for 3/2 tan(2x+135)=-(sqrt(3))/2 is x=-135/2+(5pi}{12}+\frac{pin)/2