# Trigonometry Questions

## What is the Value of Cos 54 Degrees ?

Solution : The value of cos 54 degrees is $$\sqrt{10 – 2\sqrt{5}}\over 4$$. Proof : We know that value of sin 36 degrees is $$\sqrt{10 – 2\sqrt{5}}\over 4$$. Since 54 degree is the complement of 36 degree. $$\therefore$$ cos 54 = sin(90 – 36) = sin 36 = $$\sqrt{10 – 2\sqrt{5}}\over 4$$ Hence, cos 54 …

## 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 …

## What is the Value of Sin 72 Degrees ?

Solution : The value of sin 72 degrees is $$\sqrt{10 + 2\sqrt{5}}\over 4$$. Proof : We know that value of cos 18 degrees is $$\sqrt{10 + 2\sqrt{5}}\over 4$$. Since 72 degree is the complement of 18 degree. $$\therefore$$ sin 72 = sin(90 – 18) = cos 18 = $$\sqrt{10 + 2\sqrt{5}}\over 4$$ Hence, sin 72 …