What are the components of the vector between the origin and the polar coordinate (5, (5pi)/3)?
1 Answer
Apr 7, 2016
Explanation:
To convert Polar to Cartesian coordinates , use the formulae that link them.
• x = rcostheta
• y = rsintheta here r = 5 and
theta = (5pi)/3
rArr x = 5cos((5pi)/3)" and " y = 5sin((5pi)/3)
"-----------------------------------------------------------------------" now
cos((5pi)/3) = cos(pi/3) " and " sin((5pi)/3) = -sin(pi/3) using
color(blue)" exact values for these ratios "
rArr cos(pi/3) = 1/2" and " -sin(pi/3) = -sqrt3/2
"-----------------------------------------------------------------------"
rArr x = 5cos((5pi)/3) = 5cos(pi/3) = 5xx1/2 = 5/2 and
y = 5sin((5pi)/3) = -5sin(pi/3) = -5xxsqrt3/2 = (-5sqrt3)/2
