What is the value of -6sin((2pi)/(0.8)(0.5-0.2))+15 ?

The value of -6sin((2pi)/(0.8)(0.5-0.2))+15 is -3sqrt(2)+15

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-6sin((2pi)/(0.8)(0.5-0.2))+15

Solution

- 6 sin (\frac{2 π}{0.8} (0.5 - 0.2)) + 15

Solution

- 32 + 15

Decimal Notation

10.75735 \dots

Solution steps

- 6 sin (\frac{2 π}{0.8} (0.5 - 0.2)) + 15

= - 6 sin (\frac{2 π}{\frac{4}{5}} (\frac{1}{2} - \frac{1}{5})) + 15

Simplify:

\frac{2 π}{\frac{4}{5}} (\frac{1}{2} - \frac{1}{5}) = \frac{3 π}{4}

\frac{2 π}{\frac{4}{5}} (\frac{1}{2} - \frac{1}{5})

Multiply fractions:

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

= \frac{2 π ( \frac{1}{2} - \frac{1}{5} )}{\frac{4}{5}}

Apply the fraction rule:

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

= \frac{2 π ( \frac{1}{2} - \frac{1}{5} ) \cdot 5}{4}

Multiply the numbers:

2 \cdot 5 = 10

= \frac{10 π ( \frac{1}{2} - \frac{1}{5} )}{4}

Cancel the common factor:

2

= \frac{5 π ( \frac{1}{2} - \frac{1}{5} )}{2}

Join

\frac{1}{2} - \frac{1}{5} : \frac{3}{10}

\frac{1}{2} - \frac{1}{5}

Least Common Multiplier of

2, 5 : 10

2, 5

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Multiply each factor the greatest number of times it occurs in either

2

5

= 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 10

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

10

For

\frac{1}{2} :

multiply the denominator and numerator by

5

\frac{1}{2} = \frac{1 \cdot 5}{2 \cdot 5} = \frac{5}{10}

For

\frac{1}{5} :

multiply the denominator and numerator by

2

\frac{1}{5} = \frac{1 \cdot 2}{5 \cdot 2} = \frac{2}{10}

= \frac{5}{10} - \frac{2}{10}

Since the denominators are equal, combine the fractions:

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

= \frac{5 - 2}{10}

Subtract the numbers:

5 - 2 = 3

= \frac{3}{10}

= \frac{5 π \frac{3}{10}}{2}

Multiply

5 π \frac{3}{10} : \frac{3 π}{2}

5 π \frac{3}{10}

Multiply fractions:

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

= \frac{3 \cdot 5 π}{10}

Multiply the numbers:

3 \cdot 5 = 15

= \frac{15 π}{10}

Cancel the common factor:

5

= \frac{3 π}{2}

= \frac{\frac{3 π}{2}}{2}

Apply the fraction rule:

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

= \frac{3 π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{3 π}{4}

= - 6 sin (\frac{3 π}{4}) + 15

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

sin (\frac{3 π}{4})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= - 6 \cdot \frac{2}{2} + 15

Simplify

- 6 \cdot \frac{2}{2} + 15 : - 32 + 15

- 6 \cdot \frac{2}{2} + 15

6 \cdot \frac{2}{2} = 32

6 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 6}{2}

Divide the numbers:

\frac{6}{2} = 3

= 32

= - 32 + 15

= - 32 + 15

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Frequently Asked Questions (FAQ)

What is the value of -6sin((2pi)/(0.8)(0.5-0.2))+15 ?
The value of -6sin((2pi)/(0.8)(0.5-0.2))+15 is -3sqrt(2)+15