What is the general solution for tan(4x+6)=-0.272 ?

The general solution for tan(4x+6)=-0.272 is x=-3/2+(pin)/4-(0.26557…)/4

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tan(4x+6)=-0.272

Solution

tan (4 x + 6) = - 0.272

Solution

x = - \frac{3}{2} + \frac{πn}{4} - \frac{0.26557 \dots}{4}

Degrees

x = - 89.74775 \dots^{\circ} + 4 5^{\circ} n

Solution steps

tan (4 x + 6) = - 0.272

Apply trig inverse properties

tan (4 x + 6) = - 0.272

General solutions for

tan (4 x + 6) = - 0.272

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

4 x + 6 = arctan (- 0.272) + πn

4 x + 6 = arctan (- 0.272) + πn

Solve

4 x + 6 = arctan (- 0.272) + πn : x = - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

4 x + 6 = arctan (- 0.272) + πn

Simplify

arctan (- 0.272) + πn : - arctan (\frac{34}{125}) + πn

arctan (- 0.272) + πn

arctan (- 0.272) = - arctan (\frac{34}{125})

arctan (- 0.272)

= arctan (- \frac{34}{125})

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{34}{125}) = - arctan (\frac{34}{125})

= - arctan (\frac{34}{125})

= - arctan (\frac{34}{125}) + πn

4 x + 6 = - arctan (\frac{34}{125}) + πn

Move

6

to the right side

4 x + 6 = - arctan (\frac{34}{125}) + πn

Subtract

6

from both sides

4 x + 6 - 6 = - arctan (\frac{34}{125}) + πn - 6

Simplify

4 x = - arctan (\frac{34}{125}) + πn - 6

4 x = - arctan (\frac{34}{125}) + πn - 6

Divide both sides by

4

4 x = - arctan (\frac{34}{125}) + πn - 6

Divide both sides by

4

\frac{4 x}{4} = - \frac{arctan ( \frac{34}{125} )}{4} + \frac{πn}{4} - \frac{6}{4}

Simplify

\frac{4 x}{4} = - \frac{arctan ( \frac{34}{125} )}{4} + \frac{πn}{4} - \frac{6}{4}

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

- \frac{arctan ( \frac{34}{125} )}{4} + \frac{πn}{4} - \frac{6}{4} : - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

- \frac{arctan ( \frac{34}{125} )}{4} + \frac{πn}{4} - \frac{6}{4}

Group like terms

= - \frac{6}{4} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

Cancel

\frac{6}{4} : \frac{3}{2}

\frac{6}{4}

Cancel the common factor:

2

= \frac{3}{2}

= - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

x = - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

x = - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

x = - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

x = - \frac{3}{2} + \frac{πn}{4} - \frac{arctan ( \frac{34}{125} )}{4}

Show solutions in decimal form

x = - \frac{3}{2} + \frac{πn}{4} - \frac{0.26557 \dots}{4}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for tan(4x+6)=-0.272 ?
The general solution for tan(4x+6)=-0.272 is x=-3/2+(pin)/4-(0.26557…)/4