Question

Find the exact value of cos(-7pi/4 radian).

Answer 1

cos[7pi/4]=cos(2pi−pi4)
               =cos(−pi/4)
               =cos(pi4)
               =√2/2

Answer 2

Answer:

The exact value of $\cos(-\frac{7\pi}{4})$ is $\frac{1}{\sqrt{2}}$    

Step-by-step explanation:

Given : Expression $\cos(-\frac{7\pi}{4})$ in radian.

To find : The The exact value of the given expression?

Solution :

Cos function is an even function i.e, $\cos(-x)=\cos x$

So, $\cos(-\frac{7\pi}{4})=\cos(\frac{7\pi}{4})$

Now, we convert the radian into degree, i.e, multiply by $\frac{180}{\pi}$

$=\cos(\frac{7\pi}{4}\times \frac{180}{\pi})$

$=\cos(315^\circ)$

We know, $\cos(360^\circ-\theta)=\cos \theta$      

$\cos(315^\circ)=\cos(360^\circ-45^\circ)$

$\cos(315^\circ)=\cos(45^\circ)$

The value of $\cos(45^\circ)=\frac{1}{\sqrt{2}}$

$\cos(315^\circ)=\frac{1}{\sqrt{2}}$

Therefore, The exact value of $\cos(-\frac{7\pi}{4})$ is $\frac{1}{\sqrt{2}}$