SOLUTION: Find the rectangular coordinates of the point whose polar coordinates are: {{{(matrix(1,3,-7.2,",",pi/5))}}} Round your answer to three significant digits. x = y =

Algebra ->  Trigonometry-basics -> SOLUTION: Find the rectangular coordinates of the point whose polar coordinates are: {{{(matrix(1,3,-7.2,",",pi/5))}}} Round your answer to three significant digits. x = y =       Log On


   



Question 1065323: Find the rectangular coordinates of the point
whose polar coordinates are:
%28matrix%281%2C3%2C-7.2%2C%22%2C%22%2Cpi%2F5%29%29
Round your answer to three significant digits.
x =
y =

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Find the rectangular coordinates of the point
whose polar coordinates are:
%28matrix%281%2C3%2C-7.2%2C%22%2C%22%2Cpi%2F5%29%29

That's this point:



Notice in the above graph, that θ is in QI, but
r is negative.  So we find the angle pi%2F5
in QI indicated by the dotted line and the red
arc.  But then since r = -7.2, we go 7.2 units
in the OPPOSITE direction, which puts the point
in QIII.  Now from that point, we draw a perpendicular 
up to the x-axis. 



So the x-ccordinate of the point is 

x+=+r%2Acos%28theta%29=-7%2Acos%28pi%2F5%29+=+-5.824922359

and the y-coordinate of the point is

x+=+r%2Asin%28theta%29=-7%2Asin%28pi%2F5%29+=+-4.232053817

The point in rectangular coordinates to three significant
digits is (-5.82,-4.23)

Edwin