Question

What are the components of the vector between the origin and the polar coordinate `(-6, (7pi)/8)`?

Answer 1

`x = -6 * cos ((7pi)/8) = 5.5433`

`y = -6 * sin ((7pi)/8) = - 2.2961`

Explanation:

Conversion of polar to rectangular coordinates.

`x = r cos theta, y = r sin theta`

`x = -6 * cos ((7pi)/8) = 5.5433`

`y = -6 * sin ((7pi)/8) = - 2.2961`

`tan theta = y / x = - 2.2961 / 5.5432 = tan ((7pi)/8) = -0.4142`