What is the value of 40pi[0.6+((sin(8pi*0.6))/(8pi))] ?

The value of 40pi[0.6+((sin(8pi*0.6))/(8pi))] is 24pi+(5sqrt(2)sqrt(5-\sqrt{5)})/4

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40pi[0.6+((sin(8pi*0.6))/(8pi))]

40 π [0.6 + (\frac{sin ( 8 π \cdot 0.6 )}{8 π})]

24 π + \frac{5 2 5 - 5}{4}

Solution steps

40 π [0.6 + (\frac{sin ( 8 π 0.6 )}{8 π})]

= 40 π [\frac{3}{5} + \frac{sin ( 8 π \frac{3}{5} )}{8 π}]

Simplify:

8 π \frac{3}{5} = \frac{24 π}{5}

40 π [\frac{3}{5} + \frac{sin ( \frac{24 π}{5} )}{8 π}] = 24 π + 5 sin (\frac{24 π}{5})

= 24 π + 5 sin (\frac{24 π}{5})

sin (\frac{24 π}{5}) = sin (\frac{4 π}{5})

= 24 π + 5 sin (\frac{4 π}{5})

Rewrite using trig identities:

sin (\frac{4 π}{5}) = \frac{2 5 - 5}{4}

= 24 π + 5 \cdot \frac{2 5 - 5}{4}

Simplify

24 π + 5 \cdot \frac{2 5 - 5}{4} : 24 π + \frac{5 2 5 - 5}{4}

= 24 π + \frac{5 2 5 - 5}{4}

50 cos (2 0^{\circ})

tan (arccos (\frac{6}{7}))

9 \cdot cos (3 0^{\circ})

\frac{2 - 2 sin ( \frac{π}{4} )}{cos ( \frac{π}{4} )}

100 \cdot cos (2 0^{\circ})

What is the value of 40pi[0.6+((sin(8pi*0.6))/(8pi))] ?
The value of 40pi[0.6+((sin(8pi*0.6))/(8pi))] is 24pi+(5sqrt(2)sqrt(5-\sqrt{5)})/4