What is the value of 128+127.5sin((2pi)/(16)*1) ?

The value of 128+127.5sin((2pi)/(16)*1) is (512+255sqrt(2-\sqrt{2)})/4

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128+127.5sin((2pi)/(16)*1)

128 + 127.5 sin (\frac{2 π}{16} \cdot 1)

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

Solution steps

128 + 127.5 sin (\frac{2 π}{16} \cdot 1)

= 128 + \frac{255}{2} sin (\frac{2 π}{16} \cdot 1)

Simplify:

\frac{2 π}{16} \cdot 1 = \frac{π}{8}

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

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

Rewrite using trig identities:

sin (\frac{π}{8}) = \frac{2 - 2}{2}

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

Simplify

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

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

- 5 sin (\frac{π}{4})

cosh (- πi)

arctan (\frac{60}{25})

1 + sin (3 0^{\circ})

cot (arccot (\frac{3}{3}))

What is the value of 128+127.5sin((2pi)/(16)*1) ?
The value of 128+127.5sin((2pi)/(16)*1) is (512+255sqrt(2-\sqrt{2)})/4