Find the Value of sin(3π/10)

Question:

\[ \sin\frac{3\pi}{10} \]

Solution

First convert the angle into degrees:

\[ \frac{3\pi}{10} = \frac{3\times180^\circ}{10} = 54^\circ \]

Therefore,

\[ \sin\frac{3\pi}{10} = \sin54^\circ \]

Using the standard exact value,

\[ \sin54^\circ = \cos36^\circ \]

and

\[ \cos36^\circ = \frac{1+\sqrt5}{4} \]

Hence,

\[ \sin\frac{3\pi}{10} = \frac{1+\sqrt5}{4} \]

Answer

\[ \boxed{\frac{1+\sqrt5}{4}} \]