What is the value of 128+127.5sin((2pi)/(16)*11) ?

The value of 128+127.5sin((2pi)/(16)*11) is (512-255sqrt(2+\sqrt{2)})/4

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128+127.5sin((2pi)/(16)*11)

128 + 127.5 sin (\frac{2 π}{16} \cdot 11)

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

Solution steps

128 + 127.5 sin (\frac{2 π}{16} \cdot 11)

= 128 + \frac{255}{2} sin (\frac{2 π}{16} \cdot 11)

Simplify:

\frac{2 π}{16} \cdot 11 = \frac{11 π}{8}

128 + \frac{255}{2} sin (\frac{11 π}{8}) = \frac{256 + 255 sin ( \frac{11 π}{8} )}{2}

= \frac{256 + 255 sin ( \frac{11 π}{8} )}{2}

Rewrite using trig identities:

sin (\frac{11 π}{8}) = - \frac{2 + 2}{2}

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

Simplify

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

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

178.09 sin (6 5^{\circ})

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

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

sec (2) (\frac{π}{4})

sin (\frac{19}{6})

What is the value of 128+127.5sin((2pi)/(16)*11) ?
The value of 128+127.5sin((2pi)/(16)*11) is (512-255sqrt(2+\sqrt{2)})/4