Question

What are the components of the vector between the origin and the polar coordinate `(7, pi/4)`?

Answer 1

`((7/2 sqrt2),(7/2 sqrt2))`

Explanation:

using the formulae that links Polar to Cartesian coordinates.

`• x = rcostheta`

`• y = rsintheta`

here r = 7 and `theta = pi/4`

`x = 7cos(pi/4) = 7 . 1/sqrt2 = 7/2 sqrt2`

and `y = 7sin(pi/4) = 7 . 1/sqrt2 = 7/2 sqrt2`

( using exact values for trig functions )