What is the general solution for 1-4tan(3x+1)=17 ?

The general solution for 1-4tan(3x+1)=17 is x=-(1.32581…)/3+(pin)/3-1/3

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Popular >

1-4tan(3x+1)=17

Solution

1 - 4 tan (3 x + 1) = 17

Solution

x = - \frac{1.32581 \dots}{3} + \frac{πn}{3} - \frac{1}{3}

Degrees

x = - 44.41984 \dots^{\circ} + 6 0^{\circ} n

Solution steps

1 - 4 tan (3 x + 1) = 17

Move

1

to the right side

1 - 4 tan (3 x + 1) = 17

Subtract

1

from both sides

1 - 4 tan (3 x + 1) - 1 = 17 - 1

Simplify

- 4 tan (3 x + 1) = 16

- 4 tan (3 x + 1) = 16

Divide both sides by

- 4

- 4 tan (3 x + 1) = 16

Divide both sides by

- 4

\frac{- 4 tan ( 3 x + 1 )}{- 4} = \frac{16}{- 4}

Simplify

\frac{- 4 tan ( 3 x + 1 )}{- 4} = \frac{16}{- 4}

Simplify

\frac{- 4 tan ( 3 x + 1 )}{- 4} : tan (3 x + 1)

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

Apply the fraction rule:

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

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

Divide the numbers:

\frac{4}{4} = 1

= tan (3 x + 1)

Simplify

\frac{16}{- 4} : - 4

\frac{16}{- 4}

Apply the fraction rule:

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

= - \frac{16}{4}

Divide the numbers:

\frac{16}{4} = 4

= - 4

tan (3 x + 1) = - 4

tan (3 x + 1) = - 4

tan (3 x + 1) = - 4

Apply trig inverse properties

tan (3 x + 1) = - 4

General solutions for

tan (3 x + 1) = - 4

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

3 x + 1 = arctan (- 4) + πn

3 x + 1 = arctan (- 4) + πn

Solve

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

3 x + 1 = arctan (- 4) + πn

Simplify

arctan (- 4) + πn : - arctan (4) + πn

arctan (- 4) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- 4) = - arctan (4)

= - arctan (4) + πn

3 x + 1 = - arctan (4) + πn

Move

1

to the right side

3 x + 1 = - arctan (4) + πn

Subtract

1

from both sides

3 x + 1 - 1 = - arctan (4) + πn - 1

Simplify

3 x = - arctan (4) + πn - 1

3 x = - arctan (4) + πn - 1

Divide both sides by

3

3 x = - arctan (4) + πn - 1

Divide both sides by

3

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

Simplify

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

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

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

Show solutions in decimal form

x = - \frac{1.32581 \dots}{3} + \frac{πn}{3} - \frac{1}{3}

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Frequently Asked Questions (FAQ)

What is the general solution for 1-4tan(3x+1)=17 ?
The general solution for 1-4tan(3x+1)=17 is x=-(1.32581…)/3+(pin)/3-1/3