What is the value of sin(117) ?

The value of sin(117) is (sqrt(2)sqrt(4+\sqrt{2)sqrt(5-\sqrt{5)}})/4

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sin(117)

sin (11 7^{\circ})

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

Solution steps

sin (11 7^{\circ})

Rewrite using trig identities:

sin (6 3^{\circ})

= sin (6 3^{\circ})

Rewrite using trig identities:

\frac{1 - cos ( 12 6 ^{\circ} )}{2}

= \frac{1 - cos ( 12 6 ^{\circ} )}{2}

Rewrite using trig identities:

cos (12 6^{\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}

1 - sin (\frac{11 π}{6})

sin (19 5^{\circ}) + sin (10 5^{\circ})

99 cos (1 5^{\circ})

arcsin (\frac{6}{9})

4 cos (2 0^{\circ})

What is the value of sin(117) ?
The value of sin(117) is (sqrt(2)sqrt(4+\sqrt{2)sqrt(5-\sqrt{5)}})/4