What is the value of 0.04picos(pi*1-pi*2/6) ?

The value of 0.04picos(pi*1-pi*2/6) is -pi/(50)

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0.04picos(pi1-pi2/6)

Solution

0.04 π cos (π \cdot 1 - π \cdot \frac{2}{6})

Solution

- \frac{π}{50}

Decimal Notation

- 0.06283 \dots

Solution steps

0.04 π cos (π 1 - π \frac{2}{6})

= \frac{1}{25} π cos (π 1 - π \frac{2}{6})

Simplify:

π 1 - π \frac{2}{6} = \frac{2 π}{3}

π 1 - π \frac{2}{6}

Factor out common term

π

= π (1 - \frac{2}{6})

1 - \frac{2}{6} = \frac{2}{3}

1 - \frac{2}{6}

Cancel

\frac{2}{6} : \frac{1}{3}

\frac{2}{6}

Cancel the common factor:

2

= \frac{1}{3}

= 1 - \frac{1}{3}

Convert element to fraction:

1 = \frac{1 \cdot 3}{3}

= \frac{1 \cdot 3}{3} - \frac{1}{3}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{1 \cdot 3 - 1}{3}

1 \cdot 3 - 1 = 2

1 \cdot 3 - 1

Multiply the numbers:

1 \cdot 3 = 3

= 3 - 1

Subtract the numbers:

3 - 1 = 2

= 2

= \frac{2}{3}

= π \frac{2}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 π}{3}

\frac{1}{25} π cos (\frac{2 π}{3}) = \frac{π cos ( \frac{2 π}{3} )}{25}

\frac{1}{25} π cos (\frac{2 π}{3})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 π cos ( \frac{2 π}{3} )}{25}

Multiply:

1 π = π

= \frac{π cos ( \frac{2 π}{3} )}{25}

= \frac{π cos ( \frac{2 π}{3} )}{25}

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

cos (\frac{2 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}

= \frac{π ( - \frac{1}{2} )}{25}

Simplify

\frac{π ( - \frac{1}{2} )}{25} : - \frac{π}{50}

\frac{π ( - \frac{1}{2} )}{25}

Remove parentheses:

(- a) = - a

= \frac{- π \frac{1}{2}}{25}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{π \frac{1}{2}}{25}

Multiply

π \frac{1}{2} : \frac{π}{2}

π \frac{1}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 π}{2}

Multiply:

1 π = π

= \frac{π}{2}

= - \frac{\frac{π}{2}}{25}

Simplify

\frac{\frac{π}{2}}{25} : \frac{π}{50}

\frac{\frac{π}{2}}{25}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{2 \cdot 25}

Multiply the numbers:

2 \cdot 25 = 50

= \frac{π}{50}

= - \frac{π}{50}

= - \frac{π}{50}

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Frequently Asked Questions (FAQ)

What is the value of 0.04picos(pi*1-pi*2/6) ?
The value of 0.04picos(pi*1-pi*2/6) is -pi/(50)