What is the value of 128+127.5sin((2pi)/(16)*10) ?

The value of 128+127.5sin((2pi)/(16)*10) is (512-255sqrt(2))/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

128+127.5sin((2pi)/(16)*10)

Solution

128 + 127.5 sin (\frac{2 π}{16} \cdot 10)

Solution

\frac{512 - 255 2}{4}

Decimal Notation

37.84388 \dots

Solution steps

128 + 127.5 sin (\frac{2 π}{16} \cdot 10)

= 128 + \frac{255}{2} sin (\frac{2 π}{16} \cdot 10)

Simplify:

\frac{2 π}{16} \cdot 10 = \frac{5 π}{4}

\frac{2 π}{16} \cdot 10

Multiply fractions:

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

= \frac{2 π 10}{16}

Multiply the numbers:

2 \cdot 10 = 20

= \frac{20 π}{16}

Cancel the common factor:

4

= \frac{5 π}{4}

128 + \frac{255}{2} sin (\frac{5 π}{4}) = \frac{256 + 255 sin ( \frac{5 π}{4} )}{2}

128 + \frac{255}{2} sin (\frac{5 π}{4})

Multiply

\frac{255}{2} sin (\frac{5 π}{4}) : \frac{255 sin ( \frac{5 π}{4} )}{2}

\frac{255}{2} sin (\frac{5 π}{4})

Multiply fractions:

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

= \frac{255 sin ( \frac{5 π}{4} )}{2}

= 128 + \frac{255 sin ( \frac{5 π}{4} )}{2}

Convert element to fraction:

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

= \frac{128 \cdot 2}{2} + \frac{255 sin ( \frac{5 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{5 π}{4} )}{2}

Multiply the numbers:

128 \cdot 2 = 256

= \frac{256 + 255 sin ( \frac{5 π}{4} )}{2}

= \frac{256 + 255 sin ( \frac{5 π}{4} )}{2}

Rewrite using trig identities:

sin (\frac{5 π}{4}) = - \frac{2}{2}

sin (\frac{5 π}{4})

Rewrite using trig identities:

sin (π) cos (\frac{π}{4}) + cos (π) sin (\frac{π}{4})

sin (\frac{5 π}{4})

Write

sin (\frac{5 π}{4})

sin (π + \frac{π}{4})

= sin (π + \frac{π}{4})

Use the Angle Sum identity:

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

= sin (π) cos (\frac{π}{4}) + cos (π) sin (\frac{π}{4})

= sin (π) cos (\frac{π}{4}) + cos (π) sin (\frac{π}{4})

Use the following trivial identity:

sin (π) = 0

sin (π)

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}

= 0

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

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{2}{2}

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

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}

= (- 1)

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{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}

= 0 \cdot \frac{2}{2} + (- 1) \frac{2}{2}

Simplify

= - \frac{2}{2}

= \frac{256 + 255 ( - \frac{2}{2} )}{2}

Simplify

\frac{256 + 255 ( - \frac{2}{2} )}{2} : \frac{512 - 255 2}{4}

\frac{256 + 255 ( - \frac{2}{2} )}{2}

Remove parentheses:

(- a) = - a

= \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}

Popular Examples

sec(2)(pi/4)

sec (2) (\frac{π}{4})

sin(19/6)

sin (\frac{19}{6})

tan(112)

tan (11 2^{\circ})

cos(3.29196E15)

cos (3.29196 E 1 5^{\circ})

cos((2pi)/3)-cos((4pi)/3)

cos (\frac{2 π}{3}) - cos (\frac{4 π}{3})

Frequently Asked Questions (FAQ)

What is the value of 128+127.5sin((2pi)/(16)*10) ?
The value of 128+127.5sin((2pi)/(16)*10) is (512-255sqrt(2))/4