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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}

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}

= - 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

24 \cdot cos (3 0^{\circ})

sin^{2} (8.75)

sin (3.2)

sin^{2} (2 2^{\circ})

(sin(2)(pi/2))/2

\frac{sin ( 2 ) ( \frac{π}{2} )}{2}

Frequently Asked Questions (FAQ)

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