Answer:
The exact value of [tex]\cos(-\frac{7\pi}{4})[/tex] is [tex]\frac{1}{\sqrt{2}}[/tex]
Step-by-step explanation:
Given : Expression [tex]\cos(-\frac{7\pi}{4})[/tex] in radian.
To find : The The exact value of the given expression?
Solution :
Cos function is an even function i.e, [tex]\cos(-x)=\cos x[/tex]
So, [tex]\cos(-\frac{7\pi}{4})=\cos(\frac{7\pi}{4})[/tex]
Now, we convert the radian into degree, i.e, multiply by [tex]\frac{180}{\pi}[/tex]
[tex]=\cos(\frac{7\pi}{4}\times \frac{180}{\pi})[/tex]
[tex]=\cos(315^\circ)[/tex]
We know, [tex]\cos(360^\circ-\theta)=\cos \theta[/tex]
[tex]\cos(315^\circ)=\cos(360^\circ-45^\circ)[/tex]
[tex]\cos(315^\circ)=\cos(45^\circ)[/tex]
The value of [tex]\cos(45^\circ)=\frac{1}{\sqrt{2}}[/tex]
[tex]\cos(315^\circ)=\frac{1}{\sqrt{2}}[/tex]
Therefore, The exact value of [tex]\cos(-\frac{7\pi}{4})[/tex] is [tex]\frac{1}{\sqrt{2}}[/tex]
