Answer:
Rectangular Coordinates:
![x=\frac{5\sqrt{2}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B5%5Csqrt%7B2%7D%7D%7B2%7D)
![y=\frac{5\sqrt{2}}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B5%5Csqrt%7B2%7D%7D%7B2%7D)
Step-by-step explanation:
Polar coordinate are given in the form:
![(r,\theta)](https://tex.z-dn.net/?f=%28r%2C%5Ctheta%29)
The point given is: ![(5, \frac{\pi}{4})](https://tex.z-dn.net/?f=%285%2C%20%5Cfrac%7B%5Cpi%7D%7B4%7D%29)
So,
![r=5](https://tex.z-dn.net/?f=r%3D5)
and
![\theta=\frac{\pi}{4}](https://tex.z-dn.net/?f=%5Ctheta%3D%5Cfrac%7B%5Cpi%7D%7B4%7D)
The formula to convert polar coordinates to rectangular coordinates (x, y) is:
![x=rCos \theta](https://tex.z-dn.net/?f=x%3DrCos%20%5Ctheta)
![y=rSin\theta](https://tex.z-dn.net/?f=y%3DrSin%5Ctheta)
Note that ![sin(\frac{\pi}{4})=cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}](https://tex.z-dn.net/?f=sin%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3Dcos%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D)
Thus,
![x=rCos\theta=5Cos(\frac{\pi}{4})=5*\frac{\sqrt{2}}{2}=\frac{5\sqrt{2}}{2}](https://tex.z-dn.net/?f=x%3DrCos%5Ctheta%3D5Cos%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D5%2A%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%3D%5Cfrac%7B5%5Csqrt%7B2%7D%7D%7B2%7D)
![y=rSin\theta=5*Sin(\frac{\pi}{4})=5*\frac{\sqrt{2}}{2}=\frac{5\sqrt{2}}{2}](https://tex.z-dn.net/?f=y%3DrSin%5Ctheta%3D5%2ASin%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D5%2A%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%3D%5Cfrac%7B5%5Csqrt%7B2%7D%7D%7B2%7D)
Here are the resulting percentages:
LEAH = 3.5%
RATHA = 2.3%
ED = 1.8%
CHRIS = 4.2%
MARY = 2.5%
You arrive at this answer by dividing the bonus by the wages
BONUS/WAGE = PERCENTAGE OF BONUS TO WAGE.
Chris had the greatest percentage of wages in his bonus
Step-by-step explanation:
tanX=YZ/XY
TanX=36/27=1.33
The answer to this question is Infinitely many