What is the value of ln(sec(pi/6)) ?

The value of ln(sec(pi/6)) is ln((2sqrt(3))/3)

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ln(sec(pi/6))

ln (sec (\frac{π}{6}))

ln (\frac{2 3}{3})

Decimal Notation

0.14384 \dots

Solution steps

ln (sec (\frac{π}{6}))

Use the following trivial identity:

sec (\frac{π}{6}) = \frac{2 3}{3}

sec (\frac{π}{6})

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= \frac{2 3}{3}

= ln (\frac{2 3}{3})

arctan (\frac{250}{- 185})

cos (6 0^{\circ}) - sin (4 5^{\circ})

cos (0.08)

5 \cdot cos (2 0^{\circ})

arccos (0.900405)

What is the value of ln(sec(pi/6)) ?
The value of ln(sec(pi/6)) is ln((2sqrt(3))/3)