Question

What is the exact value of cosine of the quantity pi over 3 question mark

Answer 1

We are required to find the value of the cosine of pi over 3.

The cosine of an angle is a ratio of the side adjacent to the angle to the hypothenuse side

Our approach is to first plot a triangle that will help us give values to this side and get our ratio.

Fortunately, pi over 3 is a special angle as we will see.

We can convert it to degrees via the formula:

`(\pi)/(3)*(180^o)/(\pi)=60^o`

Recall that the sum of angles in an equilateral triangle of sides' ratio 2:2:2 is 180 degrees and each angle is 60 degrees.

We can find side o through Pythagoras Theorem as:

`o=\sqrt[]{2^2-1^2}=\sqrt[]{4-1}=\sqrt[]{3}`

The cosine of the angle is a ratio of the adjacent side, o and hypothenuse, 2.

`\cos 60^o=\cos (\pi)/(3)=\frac{\text{adj}}{\text{hyp}}=(1)/(2)`

OPTION B