What is the value of 128+127.5sin((2pi)/(16)*12) ?

The value of 128+127.5sin((2pi)/(16)*12) is (256+255sin((3pi)/2))/(2)

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)*12)

128 + 127.5 sin (\frac{2 π}{16} \cdot 12)

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

Decimal Notation

0.5

Solution steps

128 + 127.5 sin (\frac{2 π}{16} \cdot 12)

= 128 + \frac{255}{2} sin (\frac{2 π}{16} \cdot 12)

Rewrite as

= sin (2 \cdot \frac{3 π}{4})

Rewrite using trig identities:

sin (2 \cdot \frac{3 π}{4}) = 2 sin (\frac{3 π}{4}) cos (\frac{3 π}{4})

sin (2 \cdot \frac{3 π}{4})

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (\frac{3 π}{4}) cos (\frac{3 π}{4})

= 128 + \frac{255}{2} sin (\frac{2 π}{16} \cdot 12)

Simplify:

\frac{2 π}{16} \cdot 12 = \frac{3 π}{2}

\frac{2 π}{16} \cdot 12

Multiply fractions:

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

= \frac{2 π 12}{16}

Multiply the numbers:

2 \cdot 12 = 24

= \frac{24 π}{16}

Cancel the common factor:

8

= \frac{3 π}{2}

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

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

Multiply

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

\frac{255}{2} sin (\frac{3 π}{2})

Multiply fractions:

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

= \frac{255 sin ( \frac{3 π}{2} )}{2}

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

Convert element to fraction:

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

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

Multiply the numbers:

128 \cdot 2 = 256

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

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

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

sec (2) (\frac{π}{4})

sin (\frac{19}{6})

tan (11 2^{\circ})

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

What is the value of 128+127.5sin((2pi)/(16)*12) ?
The value of 128+127.5sin((2pi)/(16)*12) is (256+255sin((3pi)/2))/(2)