Find the exact value of arccos sin(π/6). Explain your reasoning.

Solution:

The ratio of the lengths of the side opposite to the angle and the hypotenuse of a right-angled triangle is called the sine function which varies as the angle varies.

It is defined in the context of a right-angled triangle for acute angles.

The ratio of the lengths of the side adjacent to the angle and the hypotenuse of a right-angled triangle is called the cosine function which varies as the angle varies.

It is defined in the context of a right-angled triangle for acute angles.

We have to find the exact value of arccos sin(π/6)

We know that

sin(π/6) = 1/2

So we get,

arccos (1/2) = π/3 = 60°

Therefore, the exact value of arccos sin(π/6) is 60°.

Find the exact value of arccos sin(π/6). Explain your reasoning.

Summary:

The exact value of arccos sin(π/6) is 60°. The ratio of the lengths of the side adjacent to the angle and the hypotenuse of a right-angled triangle is called the cosine function which varies as the angle varies.