What is the general solution for tan(x-10)=-0.1 ?

The general solution for tan(x-10)=-0.1 is x=-0.09966…+180n+10

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tan(x-10)=-0.1

tan (x - 1 0^{\circ}) = - 0.1

x = - 0.09966 \dots + 18 0^{\circ} n + 1 0^{\circ}

Radians

x = - 0.09966 \dots + \frac{π}{18} + πn

Solution steps

tan (x - 1 0^{\circ}) = - 0.1

Apply trig inverse properties

tan (x - 1 0^{\circ}) = - 0.1

General solutions for

tan (x - 1 0^{\circ}) = - 0.1

tan (x) = - a \Rightarrow x = arctan (- a) + 18 0^{\circ} n

x - 1 0^{\circ} = arctan (- 0.1) + 18 0^{\circ} n

x - 1 0^{\circ} = arctan (- 0.1) + 18 0^{\circ} n

Solve

x - 1 0^{\circ} = arctan (- 0.1) + 18 0^{\circ} n : x = - arctan (\frac{1}{10}) + 18 0^{\circ} n + 1 0^{\circ}

x - 1 0^{\circ} = arctan (- 0.1) + 18 0^{\circ} n

Simplify

arctan (- 0.1) + 18 0^{\circ} n : - arctan (\frac{1}{10}) + 18 0^{\circ} n

arctan (- 0.1) + 18 0^{\circ} n

arctan (- 0.1) = - arctan (\frac{1}{10})

arctan (- 0.1)

= arctan (- \frac{1}{10})

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{1}{10}) = - arctan (\frac{1}{10})

= - arctan (\frac{1}{10})

= - arctan (\frac{1}{10}) + 18 0^{\circ} n

x - 1 0^{\circ} = - arctan (\frac{1}{10}) + 18 0^{\circ} n

Move

1 0^{\circ}

to the right side

x - 1 0^{\circ} = - arctan (\frac{1}{10}) + 18 0^{\circ} n

Add

1 0^{\circ}

to both sides

x - 1 0^{\circ} + 1 0^{\circ} = - arctan (\frac{1}{10}) + 18 0^{\circ} n + 1 0^{\circ}

Simplify

x = - arctan (\frac{1}{10}) + 18 0^{\circ} n + 1 0^{\circ}

x = - arctan (\frac{1}{10}) + 18 0^{\circ} n + 1 0^{\circ}

x = - arctan (\frac{1}{10}) + 18 0^{\circ} n + 1 0^{\circ}

Show solutions in decimal form

x = - 0.09966 \dots + 18 0^{\circ} n + 1 0^{\circ}

What is the general solution for tan(x-10)=-0.1 ?
The general solution for tan(x-10)=-0.1 is x=-0.09966…+180n+10