What is the value of sin(7/6 pi) ?

The value of sin(7/6 pi) is -1/2

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sin(7/6 pi)

sin (\frac{7}{6} π)

- \frac{1}{2}

Solution steps

sin (\frac{7}{6} π)

Simplify:

\frac{7}{6} π = \frac{7 π}{6}

= sin (\frac{7 π}{6})

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

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

Simplify

= - \frac{1}{2}

cos (8 0^{\circ}) cos (2 0^{\circ}) + sin (8 0^{\circ}) sin (2 0^{\circ})

sec (arctan (\frac{7}{8}))

cos^{4} (\frac{π}{2})

cos (11 2^{\circ})

- sin (\frac{5 π}{2})