What is the value of 128+127.5sin((2pi)/(16)*6) ?

The value of 128+127.5sin((2pi)/(16)*6) is (512+255sqrt(2))/4

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Popular >

128+127.5sin((2pi)/(16)*6)

Solution

128 + 127.5 sin (\frac{2 π}{16} \cdot 6)

Solution

\frac{512 + 255 2}{4}

Decimal Notation

218.15611 \dots

Solution steps

128 + 127.5 sin (\frac{2 π}{16} \cdot 6)

= 128 + \frac{255}{2} sin (\frac{2 π}{16} \cdot 6)

Simplify:

\frac{2 π}{16} \cdot 6 = \frac{3 π}{4}

\frac{2 π}{16} \cdot 6

Multiply fractions:

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

= \frac{2 π 6}{16}

Multiply the numbers:

2 \cdot 6 = 12

= \frac{12 π}{16}

Cancel the common factor:

4

= \frac{3 π}{4}

128 + \frac{255}{2} sin (\frac{3 π}{4}) = \frac{256 + 255 sin ( \frac{3 π}{4} )}{2}

128 + \frac{255}{2} sin (\frac{3 π}{4})

Multiply

\frac{255}{2} sin (\frac{3 π}{4}) : \frac{255 sin ( \frac{3 π}{4} )}{2}

\frac{255}{2} sin (\frac{3 π}{4})

Multiply fractions:

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

= \frac{255 sin ( \frac{3 π}{4} )}{2}

= 128 + \frac{255 sin ( \frac{3 π}{4} )}{2}

Convert element to fraction:

128 = \frac{128 \cdot 2}{2}

= \frac{128 \cdot 2}{2} + \frac{255 sin ( \frac{3 π}{4} )}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{128 \cdot 2 + 255 sin ( \frac{3 π}{4} )}{2}

Multiply the numbers:

128 \cdot 2 = 256

= \frac{256 + 255 sin ( \frac{3 π}{4} )}{2}

= \frac{256 + 255 sin ( \frac{3 π}{4} )}{2}

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}

= \frac{256 + 255 \cdot \frac{2}{2}}{2}

Simplify

\frac{256 + 255 \cdot \frac{2}{2}}{2} : \frac{512 + 255 2}{4}

\frac{256 + 255 \cdot \frac{2}{2}}{2}

Multiply

255 \cdot \frac{2}{2} : \frac{255 2}{2}

255 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 255}{2}

= \frac{256 + \frac{255 2}{2}}{2}

Join

256 + \frac{2 \cdot 255}{2} : \frac{512 + 255 2}{2}

256 + \frac{2 \cdot 255}{2}

Convert element to fraction:

256 = \frac{256 \cdot 2}{2}

= \frac{256 \cdot 2}{2} + \frac{2 \cdot 255}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{256 \cdot 2 + 2 \cdot 255}{2}

Multiply the numbers:

256 \cdot 2 = 512

= \frac{512 + 255 2}{2}

= \frac{\frac{512 + 255 2}{2}}{2}

Apply the fraction rule:

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

= \frac{512 + 2 \cdot 255}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{512 + 255 2}{4}

= \frac{512 + 255 2}{4}

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Frequently Asked Questions (FAQ)

What is the value of 128+127.5sin((2pi)/(16)*6) ?
The value of 128+127.5sin((2pi)/(16)*6) is (512+255sqrt(2))/4