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Popular >

ln(cos(pi/3))

Solution

ln (cos (\frac{π}{3}))

Solution

- ln (2)

+1

Decimal Notation

- 0.69314 \dots

Solution steps

ln (cos (\frac{π}{3}))

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

= ln (\frac{1}{2})

Simplify

ln (\frac{1}{2}) : - ln (2)

ln (\frac{1}{2})

Apply log rule:

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

= - ln (2)

= - ln (2)

Popular Examples

\frac{sin ( 4 )}{2}

1 + cos (\frac{π}{2})

cos (- 48 0^{\circ})

tan (\frac{- 5 π}{4})

arcsin(sin(-(5pi)/4))

arcsin (sin (- \frac{5 π}{4}))

Frequently Asked Questions (FAQ)

What is the value of ln(cos(pi/3)) ?
The value of ln(cos(pi/3)) is -ln(2)