Convert the polar coordinates into rectangular coordinates.?

Question

Convert the polar coordinates (5 , -4pi/3) into rectangular coordinates. 
Choices: 
(-2.50 , 4.33) 
(2.50 , -4.33) 
(4.33 , -2.50) 
(-4.33 , 2.50) 


Convert the polar coordinates (400 , 130 degrees) into rectangular coordinates. Round the rectangular coordinates to the nearest hundredth. 
Choices: 
(306.42,257.12) 
(-306.42,257.12) 
(-257.12,-306.42) 
(-257.12,306.42)

Answer 1

The polar coordinates : (r, θ) = (5, - 4π/3).

Rectangular coordinates : (x, y) = (r cos θ, r sin θ).

Where, r = 5 and θ = - 4π/3.

x = 5 cos(- 4π/3) and y = 5sin(- 4π/3)

x = 5(- 0.5) and y = 5(0.866)

x = - 2.50 and y = 4.33.

Therefore, rectangular coordinates are (- 2.50, 4.33).

First option is the correct choice.

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The polar coordinates : (r, θ) = (400, 130⁰).

Rectangular coordinates : (x, y) = (r cos θ, r sin θ).

Where, r = 400 and θ = 130⁰.

x = 400cos(130⁰) and y = 400sin(130⁰)

x = 400(- 0.6428) and y = 400(0.7660)

x = - 257.12 and y = 306.42.

Therefore, rectangular coordinates are (- 257.12, 306.42).

Fourth option is the correct choice.