What are the components of the vector between the origin and the polar coordinate #(12, (pi)/2)#?

1 Answer
Dec 26, 2015

Horizontal component is #0# and vertical component is #12#.

Explanation:

This point lies on the positive y-axis 12 units from the origin, since the polar angle is defined as an anti-clockwise turn from the positive x-axis. Hence its rectangular form is #0hati + 12hatj#.
Proof:
Convert this vector to rectangular form using the transformations from #(r,theta) to (x,y)# as follows

#x=rcostheta and y=rsintheta#

#thereforex=12cos(pi/2)=0#

#y=12sin(pi/2)=12#

This verifies its components as mentioned above.