What is the Value of Sin 54 Degrees ?

Solution :

The value of sin 54 degrees is \(\sqrt{5} + 1\over 4\).

Proof :

We know that value of cos 36 degrees is \(\sqrt{5} + 1\over 4\).

Since 54 degree is the complement of 36 degree.

\(\therefore\) sin 54 = sin(90 – 36) = cos 36 = \(\sqrt{5} + 1\over 4\)

Hence, sin 54 degrees is \(\sqrt{5} + 1\over 4\).

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