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

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

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cos((21pi)/4)

cos (\frac{21 π}{4})

- \frac{2}{2}

Solution steps

cos (\frac{21 π}{4})

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

= cos (\frac{5 π}{4})

Rewrite using trig identities:

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

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

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

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

Simplify

= - \frac{2}{2}

\frac{1}{cos ( 3 0 ^{\circ} )}

arccos (cos (\frac{π}{4}))

sin (\frac{3 π}{3})

- sin (\frac{5 π}{4})

sinh (ln (5))