What is the value of cos(81) ?

The value of cos(81) is (sqrt(2)sqrt(4-\sqrt{2)sqrt(5+\sqrt{5)}})/4

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cos(81)

cos (8 1^{\circ})

\frac{2 4 - 2 5 + 5}{4}

Solution steps

cos (8 1^{\circ})

Rewrite using trig identities:

sin (9^{\circ})

= sin (9^{\circ})

Rewrite using trig identities:

\frac{1 - cos ( 1 8 ^{\circ} )}{2}

= \frac{1 - cos ( 1 8 ^{\circ} )}{2}

Rewrite using trig identities:

cos (1 8^{\circ}) = \frac{2 5 + 5}{4}

= \frac{1 - \frac{2 5 + 5}{4}}{2}

Simplify

\frac{1 - \frac{2 5 + 5}{4}}{2} : \frac{2 4 - 2 5 + 5}{4}

= \frac{2 4 - 2 5 + 5}{4}

arccos (cos (\frac{- 5 π}{4}))

arcsin (- 3)

sin (7 1^{\circ})

sin (- 4)

- 2 cos (\frac{π}{2})

What is the value of cos(81) ?
The value of cos(81) is (sqrt(2)sqrt(4-\sqrt{2)sqrt(5+\sqrt{5)}})/4