How do you find the polar coordinates given the rectangular coordinates (4,-7)?
1 Answer
Nov 24, 2016
Explanation:
To convert from
#color(blue)"cartesian to polar coordinates"# That is
#(x,y)to(r,theta)#
#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(r=sqrt(x^2+y^2))color(white)(2/2)|)))# and
#color(red)(bar(ul(|color(white)(2/2)color(black)(theta=tan^-1(y/x))color(white)(2/2)|)))#
where# -pi < theta<=pi# Here x = 4 and y = - 7
#rArrr=sqrt(4^2+(-7)^2)=sqrt(16+49)=sqrt65# Now, (4 ,-7) is in the 4th quadrant so we must ensure that
#theta# is in the 4th quadrant.
To calculate the#color(blue)"reference angle"# we can ignore the negative.
#rArrtheta=tan^-1(7/4)=1.05larr" reference angle"# Thus
#theta=-1.05larr" in 4th quadrant"#
#rArr(4,-7)to(sqrt65,-1.05)#
