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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))

Apply rule

- (- a) = a

= ln (2)

= ln (2)

Popular Examples

(1.7*10^{-5}sin(8.9))/5

\frac{1.7 \cdot 1 0 ^{- 5} sin ( 8. 9 ^{\circ} )}{5}

cot(2pi)-1/(sec(pi/2))

cot (2 π) - \frac{1}{sec ( \frac{π}{2} )}

2(-0.54)+e^{-0.54}cos(3.27)

2 (- 0.54) + e^{- 0.54} cos (3.27)

(tan(26)+tan(28))/(1-tan(26)tan(28))

\frac{tan ( 2 6 ^{\circ} ) + tan ( 2 8 ^{\circ} )}{1 - tan ( 2 6 ^{\circ} ) tan ( 2 8 ^{\circ} )}

arctan((3.2)/(2.4))

arctan (\frac{3.2}{2.4})

Frequently Asked Questions (FAQ)

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