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

The general solution for tan(2x)=(-270-120)/(130) is x=-(1.24904…)/2+(pin)/2

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

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

x = - \frac{1.24904 \dots}{2} + \frac{πn}{2}

Radians

x = - \frac{1.24904 \dots}{2} + \frac{π}{2} n

Solution steps

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

Simplify

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

\frac{- 270 - 120}{130}

Subtract the numbers:

- 270 - 120 = - 390

= \frac{- 390}{130}

Apply the fraction rule:

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

= - \frac{390}{130}

Divide the numbers:

\frac{390}{130} = 3

= - 3

Apply trig inverse properties

tan (2 x) = - 3

General solutions for

tan (2 x) = - 3

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

2 x = arctan (- 3) + πn

2 x = arctan (- 3) + πn

Solve

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

2 x = arctan (- 3) + πn

Simplify

arctan (- 3) + πn : - arctan (3) + πn

arctan (- 3) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- 3) = - arctan (3)

= - arctan (3) + πn

2 x = - arctan (3) + πn

Divide both sides by

2

2 x = - arctan (3) + πn

Divide both sides by

2

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

Simplify

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

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

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

Show solutions in decimal form

x = - \frac{1.24904 \dots}{2} + \frac{πn}{2}

cos^{2} (θ) = \frac{2 - 3}{4}

x, θ = arctan (\frac{- 3 x}{4 y})

sin (2 x) = \frac{π}{6}

sin (x) = \frac{8}{17} sin (2 x)

2 = 1 + sin (2 x)

What is the general solution for tan(2x)=(-270-120)/(130) ?
The general solution for tan(2x)=(-270-120)/(130) is x=-(1.24904…)/2+(pin)/2