What is the general solution for tan(3x-4)=(-1)/2 ?

The general solution for tan(3x-4)=(-1)/2 is x=-(0.46364…)/3+(pin)/3+4/3

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tan(3x-4)=(-1)/2

tan (3 x - 4) = \frac{- 1}{2}

x = - \frac{0.46364 \dots}{3} + \frac{πn}{3} + \frac{4}{3}

Degrees

x = 67.53935 \dots^{\circ} + 6 0^{\circ} n

Solution steps

tan (3 x - 4) = \frac{- 1}{2}

Apply the fraction rule:

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

tan (3 x - 4) = - \frac{1}{2}

Apply trig inverse properties

tan (3 x - 4) = - \frac{1}{2}

General solutions for

tan (3 x - 4) = - \frac{1}{2}

tan (x) = - a \Rightarrow x = arctan (- a) + πn

3 x - 4 = arctan (- \frac{1}{2}) + πn

3 x - 4 = arctan (- \frac{1}{2}) + πn

Solve

3 x - 4 = arctan (- \frac{1}{2}) + πn : x = - \frac{arctan ( \frac{1}{2} )}{3} + \frac{πn}{3} + \frac{4}{3}

3 x - 4 = arctan (- \frac{1}{2}) + πn

Simplify

arctan (- \frac{1}{2}) + πn : - arctan (\frac{1}{2}) + πn

arctan (- \frac{1}{2}) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{1}{2}) = - arctan (\frac{1}{2})

= - arctan (\frac{1}{2}) + πn

3 x - 4 = - arctan (\frac{1}{2}) + πn

Move

4

to the right side

3 x - 4 = - arctan (\frac{1}{2}) + πn

Add

4

to both sides

3 x - 4 + 4 = - arctan (\frac{1}{2}) + πn + 4

Simplify

3 x = - arctan (\frac{1}{2}) + πn + 4

3 x = - arctan (\frac{1}{2}) + πn + 4

Divide both sides by

3

3 x = - arctan (\frac{1}{2}) + πn + 4

Divide both sides by

3

\frac{3 x}{3} = - \frac{arctan ( \frac{1}{2} )}{3} + \frac{πn}{3} + \frac{4}{3}

Simplify

x = - \frac{arctan ( \frac{1}{2} )}{3} + \frac{πn}{3} + \frac{4}{3}

x = - \frac{arctan ( \frac{1}{2} )}{3} + \frac{πn}{3} + \frac{4}{3}

x = - \frac{arctan ( \frac{1}{2} )}{3} + \frac{πn}{3} + \frac{4}{3}

Show solutions in decimal form

x = - \frac{0.46364 \dots}{3} + \frac{πn}{3} + \frac{4}{3}

What is the general solution for tan(3x-4)=(-1)/2 ?
The general solution for tan(3x-4)=(-1)/2 is x=-(0.46364…)/3+(pin)/3+4/3