What is the general solution for e^{(-pi)/(tan(x))}=0.6 ?

The general solution for e^{(-pi)/(tan(x))}=0.6 is x=1.40960…+pin

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Popular >

e^{(-pi)/(tan(x))}=0.6

Solution

e^{\frac{- π}{t a n ( x )}} = 0.6

Solution

x = 1.40960 \dots + πn

Degrees

x = 80.76448 \dots^{\circ} + 18 0^{\circ} n

Solution steps

e^{\frac{- π}{t a n ( x )}} = 0.6

Apply exponent rules

e^{\frac{- π}{t a n ( x )}} = 0.6

f (x) = g (x)

, then

ln (f (x)) = ln (g (x))

ln (e^{\frac{- π}{t a n ( x )}}) = ln (0.6)

Apply log rule:

ln (e^{a}) = a

ln (e^{\frac{- π}{t a n ( x )}}) = \frac{- π}{tan ( x )}

\frac{- π}{tan ( x )} = ln (0.6)

\frac{- π}{tan ( x )} = ln (0.6)

Solve

\frac{- π}{tan ( x )} = ln (0.6) : tan (x) = - \frac{π}{ln ( 0.6 )}

\frac{- π}{tan ( x )} = ln (0.6)

Simplify

\frac{- π}{tan ( x )} : - \frac{π}{tan ( x )}

\frac{- π}{tan ( x )}

Apply the fraction rule:

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

= - \frac{π}{tan ( x )}

- \frac{π}{tan ( x )} = ln (0.6)

Multiply both sides by

tan (x)

- \frac{π}{tan ( x )} = ln (0.6)

Multiply both sides by

tan (x)

- \frac{π}{tan ( x )} tan (x) = ln (0.6) tan (x)

Simplify

- π = ln (0.6) tan (x)

- π = ln (0.6) tan (x)

Switch sides

ln (0.6) tan (x) = - π

Divide both sides by

ln (0.6)

ln (0.6) tan (x) = - π

Divide both sides by

ln (0.6)

\frac{ln ( 0.6 ) tan ( x )}{ln ( 0.6 )} = \frac{- π}{ln ( 0.6 )}

Simplify

tan (x) = - \frac{π}{ln ( 0.6 )}

tan (x) = - \frac{π}{ln ( 0.6 )}

Verify Solutions

Find undefined (singularity) points:

tan (x) = 0

Take the denominator(s) of

\frac{- π}{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{π}{ln ( 0.6 )}

tan (x) = - \frac{π}{ln ( 0.6 )}

Apply trig inverse properties

tan (x) = - \frac{π}{ln ( 0.6 )}

General solutions for

tan (x) = - \frac{π}{ln ( 0.6 )}

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

x = arctan (- \frac{π}{ln ( 0.6 )}) + πn

x = arctan (- \frac{π}{ln ( 0.6 )}) + πn

Show solutions in decimal form

x = 1.40960 \dots + πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for e^{(-pi)/(tan(x))}=0.6 ?
The general solution for e^{(-pi)/(tan(x))}=0.6 is x=1.40960…+pin