What is the Value of Sin 36 Degrees ?

Solution :

The value of sin 36 degrees is \(\sqrt{10 – 2\sqrt{5}}\over 4\).

Proof :

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

Putting \(\theta\) = 36 in  \(cos \theta\) = \(\sqrt{1 – sin^2 \theta}\), we get

cos 36 = \(\sqrt{1 – sin^2 36}\) = \(\sqrt{1 – ({\sqrt{5} + 1\over 4})^2}\) = \(\sqrt{10 – 2\sqrt{5}}\over 4\)

Hence, cos 36 degrees is \(\sqrt{10 – 2\sqrt{5}}\over 4\).

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