Question

Convert z = 8cos72° + 8isin72° from polar form to rectangular form.​

Answer 1

The rectangular form of z = 8 cos72° + 8 sin72° is z = (2.5 , 7.6)

Explanation:

* Lets revise how to change from polar form to rectangular form

- Cartesian Coordinates (x , y) and Polar Coordinates (r , θ)

- Where x = r cosФ , y = r sinФ

* To convert from Polar Coordinates (r , θ) to Cartesian Coordinates (x , y)

# x = r × cos( θ )

# y = r × sin( θ )

* In the problem

∵ z = 8 cos72° + 8 sin72°

∴ r = 8

∴ Ф = 72°

∵ x = r cosФ

∴ x = 8 cos72° = 2.5

∵ y = r cosФ

∴ y = 8 sin72° = 7.6

* The rectangular form of z = 8 cos72° + 8 sin72° is z = (2.5 , 7.6)