What is the value of sin(108) ?

The value of sin(108) is (sqrt(2)sqrt(5+\sqrt{5)})/4

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sin(108)

sin (10 8^{\circ})

\frac{2 5 + 5}{4}

Solution steps

sin (10 8^{\circ})

Rewrite using trig identities:

cos (1 8^{\circ})

= cos (1 8^{\circ})

Rewrite using trig identities:

\frac{1 + cos ( 3 6 ^{\circ} )}{2}

= \frac{1 + cos ( 3 6 ^{\circ} )}{2}

Rewrite using trig identities:

cos (3 6^{\circ}) = \frac{5 + 1}{4}

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

Simplify

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

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

sec^{2} (2 π)

cos (- 42 0^{\circ})

cos (14 π)

\frac{cos ( 12 0 ^{\circ} ) + sec ( 18 0 ^{\circ} )}{csc ( 27 0 ^{\circ} ) + sin ( 33 0 ^{\circ} )}

10 \cdot cos (4 0^{\circ})

What is the value of sin(108) ?
The value of sin(108) is (sqrt(2)sqrt(5+\sqrt{5)})/4