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 \(\frac{1}{\sqrt{2}}\)
