What is the value of sin(0.1pi) ?

The value of sin(0.1pi) is (sqrt(2)sqrt(3-\sqrt{5)})/4

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sin(0.1pi)

sin (0.1 π)

\frac{2 3 - 5}{4}

Solution steps

sin (0.1 π)

= sin (\frac{1}{10} π)

Simplify:

\frac{1}{10} π = \frac{π}{10}

= sin (\frac{π}{10})

Rewrite using trig identities:

\frac{1 - cos ( \frac{π}{5} )}{2}

= \frac{1 - cos ( \frac{π}{5} )}{2}

Rewrite using trig identities:

cos (\frac{π}{5}) = \frac{5 + 1}{4}

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

Simplify

\frac{1 - \frac{5 + 1}{4}}{2} : \frac{2 3 - 5}{4}

= \frac{2 3 - 5}{4}

sin (13. 5^{\circ})

- 2 sin (\frac{7 π}{4})

arcsin (\frac{10}{16})

arccot (\frac{1}{3})

\frac{18}{cos ( 3 0 ^{\circ} )}

What is the value of sin(0.1pi) ?
The value of sin(0.1pi) is (sqrt(2)sqrt(3-\sqrt{5)})/4