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

What Is The Exact Value Of Cosine Of The Quantity Pi Over 3 Question Mark class=

Sagot :

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:

[tex]\frac{\pi}{3}\times\frac{180^o}{\pi}=60^o[/tex]

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:

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

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

[tex]\cos 60^o=\cos \frac{\pi}{3}=\frac{\text{adj}}{\text{hyp}}=\frac{1}{2}[/tex]

OPTION B

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