Question

How do you find the value of $\cos \dfrac{{9\pi }}{4}$ ?

Answer 1

Hint : In order to find the value of $\cos \dfrac{{9\pi }}{4}$ , we will rewrite $\dfrac{{9\pi }}{4}$ as $\dfrac{\pi }{4} + 2\pi$ , so as to convert to a standard trigonometric form of equation. Then, evaluate and we will use the value from the table of trigonometric ratios, by which we will get the required answer.

Complete step-by-step answer :
Now, we need to determine the value of $\cos \dfrac{{9\pi }}{4}$ .
We can rewrite $\dfrac{{9\pi }}{4}$ as $\dfrac{\pi }{4} + 2\pi$ , so as to convert to a standard trigonometric form of equation.
Thus we have,
$\cos \dfrac{{9\pi }}{4} = \cos \left( {\dfrac{\pi }{4} + 2\pi } \right)$
$= \cos \dfrac{\pi }{4}$
From the table of trigonometric ratios, we have,
$= \dfrac{{\sqrt 2 }}{2}$
Hence, the value of $\cos \dfrac{{9\pi }}{4}$ is $\dfrac{{\sqrt 2 }}{2}$ .
So, the correct answer is “ $\dfrac{{\sqrt 2 }}{2}$ ”.

Note : Whenever we are facing these types of problems the knowledge of values of trigonometric table ratios is important. Trigonometric table involves the relationship with the length and angles of the triangle. It is generally associated with the right-angled triangle, where one of the angles is always $90^\circ$ .
Trigonometric ratios table helps to find the values of trigonometric standard angles $0^\circ ,\,30^\circ ,\,45^\circ ,\,60^\circ \,,90^\circ$ . It consists of sine, cosine, tangent, cosecant, secant, cotangent. The trigonometric table was the reason for the most digital development to take place at this rate today as the first mechanical computing devices found application through careful use of trigonometry.