Trigonometry Polar Coordinates 2

Question 1

What is the polar form of the point (−3, 0) in rectangular coordinates?

Accepted Answer

(3, 180°)

Answer

The point (−3, 0) lies on the negative x-axis, so r = 3 and θ = 180°.

Question 2

Which polar equation represents a circle of radius 5 centered at the origin?

Accepted Answer

r = 5

Answer

r = 5 is a circle centered at the origin with radius 5 in polar coordinates.

Question 3

Convert r = 6 sin θ to rectangular form.

Accepted Answer

x² + (y − 3)² = 9

Answer

Multiply both sides by r: r² = 6r sin θ → x² + y² = 6y → x² + (y−3)² = 9.

Question 4

What is the distance between polar points (4, 30°) and (4, 150°)?

Accepted Answer

4√3

Answer

Using the polar distance formula: d² = 16 + 16 − 2(16)cos(120°) = 48, so d = 4√3.

Question 5

The polar curve r = 1 + sin θ is called a:

Accepted Answer

Cardioid

Answer

r = 1 + sin θ is a cardioid, a special limaçon where the added constant equals the coefficient of sin θ.

Trigonometry Practice Test