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

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

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

\frac{512 - 255 2}{4}

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}

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

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

Simplify

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

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

sec (2) (\frac{π}{4})

sin (\frac{19}{6})

tan (11 2^{\circ})

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

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

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