What is the value of pi/6+ln|sin(pi/6)| ?

The value of pi/6+ln|sin(pi/6)| is pi/6-ln(2)

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pi/6+ln|sin(pi/6)|

\frac{π}{6} + ln sin (\frac{π}{6})

\frac{π}{6} - ln (2)

Decimal Notation

- 0.16954 \dots

Solution steps

\frac{π}{6} + ln sin (\frac{π}{6})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{π}{6} + ln \frac{1}{2}

Simplify

\frac{π}{6} + ln \frac{1}{2} : \frac{π}{6} - ln (2)

\frac{π}{6} + ln \frac{1}{2}

Simplify

\frac{1}{2} : \frac{1}{2}

\frac{1}{2}

Apply absolute rule:

∣ a ∣ = a, a \geq 0

\frac{1}{2} = \frac{1}{2}

= \frac{1}{2}

= \frac{π}{6} + ln (\frac{1}{2})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= \frac{π}{6} - ln (2)

= \frac{π}{6} - ln (2)

\frac{sin ( 2 ( - 0.1 ) )}{- 0.1}

arccos (\frac{16}{261})

(sin (\frac{π}{4}) cos (\frac{π}{6}) - sin (\frac{π}{6}) cos (\frac{π}{4}))^{2}

arctan (\frac{17}{2})

sec (\frac{- 7 π}{3})

What is the value of pi/6+ln|sin(pi/6)| ?
The value of pi/6+ln|sin(pi/6)| is pi/6-ln(2)