What is the general solution for 2tan(2x+10)=-5.5 ?

The general solution for 2tan(2x+10)=-5.5 is x=-5+(pin)/2-(1.22202…)/2

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2tan(2x+10)=-5.5

Solution

2 tan (2 x + 10) = - 5.5

Solution

x = - 5 + \frac{πn}{2} - \frac{1.22202 \dots}{2}

Degrees

x = - 321.48734 \dots^{\circ} + 9 0^{\circ} n

Solution steps

2 tan (2 x + 10) = - 5.5

Divide both sides by

2

2 tan (2 x + 10) = - 5.5

Divide both sides by

2

\frac{2 tan ( 2 x + 10 )}{2} = \frac{- 5.5}{2}

Simplify

\frac{2 tan ( 2 x + 10 )}{2} = \frac{- 5.5}{2}

Simplify

\frac{2 tan ( 2 x + 10 )}{2} : tan (2 x + 10)

\frac{2 tan ( 2 x + 10 )}{2}

Divide the numbers:

\frac{2}{2} = 1

= tan (2 x + 10)

Simplify

\frac{- 5.5}{2} : - 2.75

\frac{- 5.5}{2}

Apply the fraction rule:

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

= - \frac{5.5}{2}

Divide the numbers:

\frac{5.5}{2} = 2.75

= - 2.75

tan (2 x + 10) = - 2.75

tan (2 x + 10) = - 2.75

tan (2 x + 10) = - 2.75

Apply trig inverse properties

tan (2 x + 10) = - 2.75

General solutions for

tan (2 x + 10) = - 2.75

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

2 x + 10 = arctan (- 2.75) + πn

2 x + 10 = arctan (- 2.75) + πn

Solve

2 x + 10 = arctan (- 2.75) + πn : x = - 5 + \frac{πn}{2} - \frac{arctan ( \frac{11}{4} )}{2}

2 x + 10 = arctan (- 2.75) + πn

Simplify

arctan (- 2.75) + πn : - arctan (\frac{11}{4}) + πn

arctan (- 2.75) + πn

arctan (- 2.75) = - arctan (\frac{11}{4})

arctan (- 2.75)

= arctan (- \frac{11}{4})

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{11}{4}) = - arctan (\frac{11}{4})

= - arctan (\frac{11}{4})

= - arctan (\frac{11}{4}) + πn

2 x + 10 = - arctan (\frac{11}{4}) + πn

Move

10

to the right side

2 x + 10 = - arctan (\frac{11}{4}) + πn

Subtract

10

from both sides

2 x + 10 - 10 = - arctan (\frac{11}{4}) + πn - 10

Simplify

2 x = - arctan (\frac{11}{4}) + πn - 10

2 x = - arctan (\frac{11}{4}) + πn - 10

Divide both sides by

2

2 x = - arctan (\frac{11}{4}) + πn - 10

Divide both sides by

2

\frac{2 x}{2} = - \frac{arctan ( \frac{11}{4} )}{2} + \frac{πn}{2} - \frac{10}{2}

Simplify

\frac{2 x}{2} = - \frac{arctan ( \frac{11}{4} )}{2} + \frac{πn}{2} - \frac{10}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

- \frac{arctan ( \frac{11}{4} )}{2} + \frac{πn}{2} - \frac{10}{2} : - 5 + \frac{πn}{2} - \frac{arctan ( \frac{11}{4} )}{2}

- \frac{arctan ( \frac{11}{4} )}{2} + \frac{πn}{2} - \frac{10}{2}

Group like terms

= - \frac{10}{2} + \frac{πn}{2} - \frac{arctan ( \frac{11}{4} )}{2}

Divide the numbers:

\frac{10}{2} = 5

= - 5 + \frac{πn}{2} - \frac{arctan ( \frac{11}{4} )}{2}

x = - 5 + \frac{πn}{2} - \frac{arctan ( \frac{11}{4} )}{2}

x = - 5 + \frac{πn}{2} - \frac{arctan ( \frac{11}{4} )}{2}

x = - 5 + \frac{πn}{2} - \frac{arctan ( \frac{11}{4} )}{2}

x = - 5 + \frac{πn}{2} - \frac{arctan ( \frac{11}{4} )}{2}

Show solutions in decimal form

x = - 5 + \frac{πn}{2} - \frac{1.22202 \dots}{2}

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Frequently Asked Questions (FAQ)

What is the general solution for 2tan(2x+10)=-5.5 ?
The general solution for 2tan(2x+10)=-5.5 is x=-5+(pin)/2-(1.22202…)/2