Answer:
Rectangular Coordinates:
[tex]x=\frac{5\sqrt{2}}{2}[/tex]
[tex]y=\frac{5\sqrt{2}}{2}[/tex]
Step-by-step explanation:
Polar coordinate are given in the form:
[tex](r,\theta)[/tex]
The point given is: [tex](5, \frac{\pi}{4})[/tex]
So,
[tex]r=5[/tex]
and
[tex]\theta=\frac{\pi}{4}[/tex]
The formula to convert polar coordinates to rectangular coordinates (x, y) is:
[tex]x=rCos \theta[/tex]
[tex]y=rSin\theta[/tex]
Note that [tex]sin(\frac{\pi}{4})=cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}[/tex]
Thus,
[tex]x=rCos\theta=5Cos(\frac{\pi}{4})=5*\frac{\sqrt{2}}{2}=\frac{5\sqrt{2}}{2}[/tex]
[tex]y=rSin\theta=5*Sin(\frac{\pi}{4})=5*\frac{\sqrt{2}}{2}=\frac{5\sqrt{2}}{2}[/tex]
