What is the value of 0.01cos((2pi)/(1.2)(4-0.3)) ?

The value of 0.01cos((2pi)/(1.2)(4-0.3)) is (sqrt(3))/(200)

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0.01cos((2pi)/(1.2)(4-0.3))

Solution

0.01 cos (\frac{2 π}{1.2} (4 - 0.3))

Solution

\frac{3}{200}

Decimal Notation

0.00866 \dots

Solution steps

0.01 cos (\frac{2 π}{1.2} (4 - 0.3))

= \frac{1}{100} cos (\frac{2 π}{\frac{6}{5}} (4 - \frac{3}{10}))

Simplify:

\frac{2 π}{\frac{6}{5}} (4 - \frac{3}{10}) = \frac{37 π}{6}

\frac{2 π}{\frac{6}{5}} (4 - \frac{3}{10})

Multiply fractions:

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

= \frac{2 π ( 4 - \frac{3}{10} )}{\frac{6}{5}}

Apply the fraction rule:

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

= \frac{2 π ( 4 - \frac{3}{10} ) \cdot 5}{6}

Multiply the numbers:

2 \cdot 5 = 10

= \frac{10 π ( - \frac{3}{10} + 4 )}{6}

Cancel the common factor:

2

= \frac{5 π ( - \frac{3}{10} + 4 )}{3}

Join

- \frac{3}{10} + 4 : \frac{37}{10}

- \frac{3}{10} + 4

Convert element to fraction:

4 = \frac{4 \cdot 10}{10}

= - \frac{3}{10} + \frac{4 \cdot 10}{10}

Since the denominators are equal, combine the fractions:

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

= \frac{- 3 + 4 \cdot 10}{10}

- 3 + 4 \cdot 10 = 37

- 3 + 4 \cdot 10

Multiply the numbers:

4 \cdot 10 = 40

= - 3 + 40

Add/Subtract the numbers:

- 3 + 40 = 37

= 37

= \frac{37}{10}

= \frac{5 π \frac{37}{10}}{3}

Multiply

5 π \frac{37}{10} : \frac{37 π}{2}

5 π \frac{37}{10}

Multiply fractions:

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

= \frac{37 \cdot 5 π}{10}

Multiply the numbers:

37 \cdot 5 = 185

= \frac{185 π}{10}

Cancel the common factor:

5

= \frac{37 π}{2}

= \frac{\frac{37 π}{2}}{3}

Apply the fraction rule:

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

= \frac{37 π}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{37 π}{6}

\frac{1}{100} cos (\frac{37 π}{6}) = \frac{cos ( \frac{37 π}{6} )}{100}

\frac{1}{100} cos (\frac{37 π}{6})

Multiply fractions:

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

= \frac{1 \cdot cos ( \frac{37 π}{6} )}{100}

Multiply:

1 \cdot cos (\frac{37 π}{6}) = cos (\frac{37 π}{6})

= \frac{cos ( \frac{37 π}{6} )}{100}

= \frac{cos ( \frac{37 π}{6} )}{100}

cos (\frac{37 π}{6}) = cos (\frac{π}{6})

cos (\frac{37 π}{6})

Rewrite

\frac{37 π}{6}

2 π \cdot 3 + \frac{π}{6}

= cos (2 π 3 + \frac{π}{6})

Apply the periodicity of

cos

cos (x + 2 π \cdot k) = cos (x)

cos (2 π \cdot 3 + \frac{π}{6}) = cos (\frac{π}{6})

= cos (\frac{π}{6})

= \frac{cos ( \frac{π}{6} )}{100}

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{π}{6})

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{3}{2}

= \frac{\frac{3}{2}}{100}

Simplify

\frac{\frac{3}{2}}{100} : \frac{3}{200}

\frac{\frac{3}{2}}{100}

Apply the fraction rule:

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

= \frac{3}{2 \cdot 100}

Multiply the numbers:

2 \cdot 100 = 200

= \frac{3}{200}

= \frac{3}{200}

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Frequently Asked Questions (FAQ)

What is the value of 0.01cos((2pi)/(1.2)(4-0.3)) ?
The value of 0.01cos((2pi)/(1.2)(4-0.3)) is (sqrt(3))/(200)