Answer :
Answer:
Explanation:
a) cos (7/4π)
We simplify the given trigonometric function first to express it into a surd. Surd means when we can't simplify a number to remove a square root or has a decimal which goes on forever without repeating.
For the given the given function:
[tex]\begin{gathered} \cos (\frac{7}{4}\pi)=\cos (\pi+\frac{3\pi}{4}) \\ \\ \\ \end{gathered}[/tex]Using the identity:
cos(x+y)=cos(x)cos(y)-sin(x)sin(y)
So,
[tex]\begin{gathered} =\cos (\pi)\cos (\frac{3\pi}{4})-\sin (\pi)\sin (\frac{3\pi}{4}) \\ \end{gathered}[/tex]Since:
[tex]\begin{gathered} \cos (\pi)=-1 \\ \sin (\pi)=0 \\ \cos (\frac{3\pi}{4})=-\frac{\sqrt[]{2}}{2} \\ \sin (\frac{3\pi}{4})=\frac{\sqrt[]{2}}{2} \end{gathered}[/tex]Simplify and rearrange
[tex]\begin{gathered} =\cos (\pi)\cos (\frac{3\pi}{4})-\sin (\pi)\sin (\frac{3\pi}{4}) \\ =(-1)(-\frac{\sqrt[]{2}}{2})-(0)(\frac{\sqrt[]{2}}{2}) \\ \text{Calculate} \\ =\frac{\sqrt[]{2}}{2} \end{gathered}[/tex]Therefore,
[tex]\cos (\frac{7\pi}{4})=\frac{\sqrt[]{2}}{2}[/tex]