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.

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