What is the value of sin((21pi)/4) ?

The value of sin((21pi)/4) is -(sqrt(2))/2

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sin((21pi)/4)

sin (\frac{21 π}{4})

- \frac{2}{2}

Solution steps

sin (\frac{21 π}{4})

sin (\frac{21 π}{4}) = sin (\frac{5 π}{4})

= sin (\frac{5 π}{4})

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

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

Simplify

= - \frac{2}{2}

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