What is the value of cos((5pi)/(24)) ?

The value of cos((5pi)/(24)) is (sqrt(2)sqrt(4+\sqrt{6)-sqrt(2)})/4

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cos((5pi)/(24))

cos (\frac{5 π}{24})

\frac{2 4 + 6 - 2}{4}

Solution steps

cos (\frac{5 π}{24})

Rewrite using trig identities:

\frac{1 + cos ( \frac{5 π}{12} )}{2}

= \frac{1 + cos ( \frac{5 π}{12} )}{2}

Rewrite using trig identities:

cos (\frac{5 π}{12}) = \frac{6 - 2}{4}

= \frac{1 + \frac{6 - 2}{4}}{2}

Simplify

\frac{1 + \frac{6 - 2}{4}}{2} : \frac{2 4 + 6 - 2}{4}

= \frac{2 4 + 6 - 2}{4}

250 cos (6 0^{\circ})

cos (\frac{17}{12} π)

arcsin (\frac{2}{5})

tan (arcsin (\frac{3}{4}) - arccos (\frac{1}{3}))

sin (15 6^{\circ})

What is the value of cos((5pi)/(24)) ?
The value of cos((5pi)/(24)) is (sqrt(2)sqrt(4+\sqrt{6)-sqrt(2)})/4