What is the value of sin((9pi)/6) ?

The value of sin((9pi)/6) is -1

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sin((9pi)/6)

sin (\frac{9 π}{6})

- 1

Solution steps

sin (\frac{9 π}{6})

Simplify:

\frac{9 π}{6} = \frac{3 π}{2}

= sin (\frac{3 π}{2})

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

cos (\frac{π}{2}) = 0

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

sin (\frac{π}{2}) = 1

= 0 \cdot 0 + (- 1) \cdot 1

Simplify

= - 1

cos (67.3 8^{\circ})

1 - sin (\frac{7 π}{6})

sin (\frac{4 π}{9})

cos (arccos (2))

cos (\frac{15 π}{2})