What is the value of sin((35pi)/6) ?

The value of sin((35pi)/6) is -1/2

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sin((35pi)/6)

sin (\frac{35 π}{6})

- \frac{1}{2}

Solution steps

sin (\frac{35 π}{6})

sin (\frac{35 π}{6}) = sin (\frac{11 π}{6})

= sin (\frac{11 π}{6})

Rewrite using trig identities:

sin (π) cos (\frac{5 π}{6}) + cos (π) sin (\frac{5 π}{6})

= sin (π) cos (\frac{5 π}{6}) + cos (π) sin (\frac{5 π}{6})

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

= 0 \cdot (- \frac{3}{2}) + (- 1) \frac{1}{2}

Simplify

= - \frac{1}{2}

cos (15 0^{\circ}) + sin (4 5^{\circ}) + \frac{1}{2} cot (- 33 0^{\circ})

arctan (\frac{8 3}{- 8})

- e^{0} cos (0)

cos (6 \cdot π)

cos (15 5^{\circ}) cos (2 0^{\circ}) + sin (15 5^{\circ}) sin (2 0^{\circ})