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

1 Answer
Trevor Ryan.
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.

Related questions
See all questions in Component Vectors
Impact of this question
1722 views around the world
You can reuse this answer
Creative Commons License