What is expand sin(8(pi/6+(pin)/4)) ?

The solution to expand sin(8(pi/6+(pin)/4)) is -(sqrt(3))/2

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expand sin(8(pi/6+(pin)/4))

expand

sin (8 (\frac{π}{6} + \frac{πn}{4}))

- \frac{3}{2}

Decimal Notation

- 0.86602 \dots

Solution steps

sin (8 (\frac{π}{6} + \frac{πn}{4}))

Expand

8 (\frac{π}{6} + \frac{πn}{4}) : \frac{4 π}{3} + 2 πn

= sin (\frac{4 π}{3} + 2 πn)

Rewrite using trig identities

= - \frac{3}{2} cos (2 πn) - \frac{1}{2} sin (2 πn)

Rewrite using trig identities

= - \frac{3}{2}

(2 x^{3} - 128) (x - 2)

(5 \cdot i + 2)^{4}

(x^{2} + 21 - 5) (x^{2} - x - 2)

(1 + i)^{21}

(5 x + 4 y = 1, 7) (y - x = 2)

What is expand sin(8(pi/6+(pin)/4)) ?
The solution to expand sin(8(pi/6+(pin)/4)) is -(sqrt(3))/2