Question

How do you find the exact value of $\cos 8\pi$?

Answer 1

Hint: As we know that $\pi$ is the symbol used to represent the ratio of a circle’s circumference to its diameter. Now, we will use the concept of circle and find the value of $\cos 8\pi$.

Complete step by step answer:
We have to find the exact value of $\cos 8\pi$.
Now, we know that the sum of the central angle of a circle is equal to $360{}^{\circ }$. It means if we go once around the circle we go through an angle $2\pi$. Now, we know that cosine is the circular function so we will get
$\cos 2\pi =1$
Now, if we go the second time through the circle we get the angle as $4\pi$.
Similarly if we go third time through the circle we get the angle as $6\pi$.
Finally if we go through the circle fourth time we get the angle as $8\pi$.
But after the four revolutions we are at the same point where we started so the value of cosine function remains the same.

So we will get $\cos 8\pi =1$.

Note: Pi was first described as the quantity which, when multiplied by diameter of the circle gives the circumference of the circle. The value of $\pi$ is given as ${\displaystyle \frac{22}{7}}$ or $3.14$. Students may try to find the value of $\cos 8\pi$ by putting the value of $\pi$ which is a wrong way to solve and doesn’t give any answer.