en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometry >

-ln(cos(pi/3))

Solution

- ln (cos (\frac{π}{3}))

Solution

ln (2)

+1

Decimal

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

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

cos((0.577)/(53.2))

(cos(25))/(cos(32))

Frequently Asked Questions (FAQ)

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