What is the value of 128+127.5sin((2pi)/(16)*4) ?

The value of 128+127.5sin((2pi)/(16)*4) is 511/2

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128+127.5sin((2pi)/(16)*4)

128 + 127.5 sin (\frac{2 π}{16} \cdot 4)

\frac{511}{2}

Decimal Notation

255.5

Solution steps

128 + 127.5 sin (\frac{2 π}{16} \cdot 4)

= 128 + \frac{255}{2} sin (\frac{2 π}{16} \cdot 4)

Simplify:

\frac{2 π}{16} \cdot 4 = \frac{π}{2}

\frac{2 π}{16} \cdot 4

Multiply fractions:

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

= \frac{2 π 4}{16}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{8 π}{16}

Cancel the common factor:

8

= \frac{π}{2}

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

128 + \frac{255}{2} sin (\frac{π}{2})

Multiply

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

\frac{255}{2} sin (\frac{π}{2})

Multiply fractions:

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

= \frac{255 sin ( \frac{π}{2} )}{2}

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

Convert element to fraction:

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

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

Multiply the numbers:

128 \cdot 2 = 256

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

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

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

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}

= 1

= \frac{256 + 255 \cdot 1}{2}

Simplify

= \frac{511}{2}

arccot (\frac{8}{15})

4 \cdot sin (\frac{π}{2})

10 sin (π^{0.29})

csc (\frac{π}{3}) - cos (\frac{π}{4})

sin^{2} (9)

What is the value of 128+127.5sin((2pi)/(16)*4) ?
The value of 128+127.5sin((2pi)/(16)*4) is 511/2