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

The value of 128+127.5sin((2pi)/(16)*3) is (512+255sqrt(2+\sqrt{2)})/4

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128+127.5sin((2pi)/(16)*3)

128 + 127.5 sin (\frac{2 π}{16} \cdot 3)

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

Solution steps

128 + 127.5 sin (\frac{2 π}{16} \cdot 3)

= 128 + \frac{255}{2} sin (\frac{2 π}{16} \cdot 3)

Simplify:

\frac{2 π}{16} \cdot 3 = \frac{3 π}{8}

128 + \frac{255}{2} sin (\frac{3 π}{8}) = \frac{256 + 255 sin ( \frac{3 π}{8} )}{2}

= \frac{256 + 255 sin ( \frac{3 π}{8} )}{2}

Rewrite using trig identities:

sin (\frac{3 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}

sin (41. 8^{\circ})

(cos (\frac{3 π}{4}) + i sin (\frac{3 π}{4}))^{4}

arctan (\frac{9}{400})

sinh (iπ)

10 + 4 cos (2 \cdot 0.31616)

What is the value of 128+127.5sin((2pi)/(16)*3) ?
The value of 128+127.5sin((2pi)/(16)*3) is (512+255sqrt(2+\sqrt{2)})/4