What is the value of sin((17pi)/(12)) ?

The value of sin((17pi)/(12)) is (-sqrt(2)-sqrt(6))/4

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sin((17pi)/(12))

sin (\frac{17 π}{12})

\frac{- 2 - 6}{4}

Solution steps

sin (\frac{17 π}{12})

Rewrite using trig identities:

sin (\frac{3 π}{4}) cos (\frac{2 π}{3}) + cos (\frac{3 π}{4}) sin (\frac{2 π}{3})

= sin (\frac{3 π}{4}) cos (\frac{2 π}{3}) + cos (\frac{3 π}{4}) sin (\frac{2 π}{3})

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

= \frac{2}{2} (- \frac{1}{2}) + (- \frac{2}{2}) \frac{3}{2}

Simplify

\frac{2}{2} (- \frac{1}{2}) + (- \frac{2}{2}) \frac{3}{2} : \frac{- 2 - 6}{4}

= \frac{- 2 - 6}{4}

sin (x) = - 1

\frac{cos ( 3 x )}{cos ( x )} = 1 - 4 sin^{2} (x)

cos (- 2 π)

sin (θ) = cos (θ)

cot (θ) - 1 = 0

What is the value of sin((17pi)/(12)) ?
The value of sin((17pi)/(12)) is (-sqrt(2)-sqrt(6))/4