Find the rectangular coordinates of the point (squareroot3, pi/6)

The rectangular coordinates of the point are (3/2 , √3/2)

Step-by-step explanation:

* Lets study how to change from polar form to rectangular coordinates

- To convert from polar form (r , Ф) to rectangular coordinates (x , y)

 use these rules

# x = r cos Ф

# y = r sin Ф

* Now lets solve the problem

∵ The point in the rectangular coordinates is (√3 , π/6)

∴ r = √3 and Ф = π/6

- Lets find the x-coordinates

∵ x = r cos Ф

∵ r = √3

∵ Ф = π/6

∴ x = √3 cos π/6

∵ cos π/6 = √3/2

∴ x = √3 (√3/2) = 3/2

* The x-coordinate of the point is 3/2

- Lets find the y-coordinates

∵ y = r sin Ф

∵ r = √3

∵ Ф = π/6

∴ y = √3 sin π/6

∵ sin π/6 = 1/2

∴ y = √3 (1/2) = √3/2

* The y-coordinate of the point is √3/2

∴ The rectangular coordinates of the point are (3/2 , √3/2)

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