What is the general solution for tan(2x)=(130)/(-270-120) ?

The general solution for tan(2x)=(130)/(-270-120) is x=-(0.32175…)/2+(pin)/2

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tan(2x)=(130)/(-270-120)

tan (2 x) = \frac{130}{- 270 - 120}

x = - \frac{0.32175 \dots}{2} + \frac{πn}{2}

Radians

x = - \frac{0.32175 \dots}{2} + \frac{π}{2} n

Solution steps

tan (2 x) = \frac{130}{- 270 - 120}

Simplify

\frac{130}{- 270 - 120} : - \frac{1}{3}

\frac{130}{- 270 - 120}

Subtract the numbers:

- 270 - 120 = - 390

= \frac{130}{- 390}

Apply the fraction rule:

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

= - \frac{130}{390}

Cancel the common factor:

130

= - \frac{1}{3}

Apply trig inverse properties

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

General solutions for

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

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

2 x = arctan (- \frac{1}{3}) + πn

2 x = arctan (- \frac{1}{3}) + πn

Solve

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

2 x = arctan (- \frac{1}{3}) + πn

Simplify

arctan (- \frac{1}{3}) + πn : - arctan (\frac{1}{3}) + πn

arctan (- \frac{1}{3}) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{1}{3}) = - arctan (\frac{1}{3})

= - arctan (\frac{1}{3}) + πn

2 x = - arctan (\frac{1}{3}) + πn

Divide both sides by

2

2 x = - arctan (\frac{1}{3}) + πn

Divide both sides by

2

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

Simplify

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

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

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

Show solutions in decimal form

x = - \frac{0.32175 \dots}{2} + \frac{πn}{2}

- 3 sin (x) - 2 cos (2 x) = 0

2 cos (x) tan (x) = 1

sin (10 x) = sin (7 x)

185 = \frac{220 2}{π} - cos (π) + cos (x)

x, 2 sin^{2} (x) = sin (x)

What is the general solution for tan(2x)=(130)/(-270-120) ?
The general solution for tan(2x)=(130)/(-270-120) is x=-(0.32175…)/2+(pin)/2