What is the general solution for 2.55= 1/(tan(x)) ?

The general solution for 2.55= 1/(tan(x)) is x=0.37372…+pin

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Popular Trigonometry >

2.55= 1/(tan(x))

Solution

2.55 = \frac{1}{tan ( x )}

Solution

x = 0.37372 \dots + πn

Degrees

x = 21.41296 \dots^{\circ} + 18 0^{\circ} n

Solution steps

2.55 = \frac{1}{tan ( x )}

Switch sides

\frac{1}{tan ( x )} = 2.55

Multiply both sides by

tan (x)

\frac{1}{tan ( x )} = 2.55

Multiply both sides by

tan (x)

\frac{1}{tan ( x )} tan (x) = 2.55 tan (x)

Simplify

1 = 2.55 tan (x)

1 = 2.55 tan (x)

Switch sides

2.55 tan (x) = 1

Multiply both sides by

100

2.55 tan (x) = 1

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

2.55 tan (x) \cdot 100 = 1 \cdot 100

Refine

255 tan (x) = 100

255 tan (x) = 100

Divide both sides by

255

255 tan (x) = 100

Divide both sides by

255

\frac{255 tan ( x )}{255} = \frac{100}{255}

Simplify

tan (x) = \frac{20}{51}

tan (x) = \frac{20}{51}

Verify Solutions

Find undefined (singularity) points:

tan (x) = 0

Take the denominator(s) of

\frac{1}{tan ( x )}

and compare to zero

tan (x) = 0

The following points are undefined

tan (x) = 0

Combine undefined points with solutions:

tan (x) = \frac{20}{51}

Apply trig inverse properties

tan (x) = \frac{20}{51}

General solutions for

tan (x) = \frac{20}{51}

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

x = arctan (\frac{20}{51}) + πn

x = arctan (\frac{20}{51}) + πn

Show solutions in decimal form

x = 0.37372 \dots + πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 2.55= 1/(tan(x)) ?
The general solution for 2.55= 1/(tan(x)) is x=0.37372…+pin