CONVERTING BETWEEN POLAR AND RECTANGULAR COORDINATES WORKSHEET

Problems 1-5 : Convert the given polar coordinates to rectangular coordinates.

Problem 1 :

Problem 2 :

(-4, 45°)

Problem 3 :

Problem 4 :

Problem 5 :

(8, 510°)

Problems 6-12 : Convert the given rectangular coordinates to polar coordinates.

Problem 6 :

(2, √2)

Give the value of θ in radians.

Problem 7 :

(-1, √3)

Give the value of θ in radians.

Problem 8 :

(2, -2)

Give the value of θ in degrees.

Problem 9 :

(0, -5)

Give the value of θ in radians.

Problem 10 :

(-3, 0)

Give the value of θ in degrees.

Problem 11 :

(7, 0)

Give the value of θ in degrees.

Problem 12 :

(-4, 3)

Give the value of θ in degrees.

Answers

1. Answer :

The rectangular coordinates are

(2, 2√3)

2. Answer :

(-4, 45°)

The rectangular coordinates are (-2√2, -2√2).

3. Answer :

The rectangular coordinates are

(-3√3, -3)

4. Answer :

The rectangular coordinates are

(5, -5√3)

5. Answer :

(8, 510°)

The rectangular coordinates are

(-4, 4√3)

6. Answer :

(2, √2)

The value of r :

The value of θ :

The point (2, √2) is in I^st quadrant. Then, we have

θ = α

The polar coordinates are

7. Answer :

(-1, √3)

The value of r :

The value of θ :

The point (-1, √3) is in II^nd Quadrant. Then, we have

θ = π - α