Trigonometry Polar Coordinates 3

Question 1

What is the rectangular equivalent of the polar point (2√2, 225°)?

Accepted Answer

(−2, −2)

Answer

x = 2√2·cos 225° = 2√2·(−√2/2) = −2, y = 2√2·sin 225° = −2, giving (−2, −2).

Question 2

How many petals does the rose curve r = cos(5θ) have?

Accepted Answer

5

Answer

r = cos(nθ) has n petals when n is odd.

Question 3

The polar equation r = 4/(1 + cos θ) represents which conic section?

Accepted Answer

Parabola

Answer

When e = 1 in r = ed/(1 + e cos θ), the conic is a parabola.

Question 4

Evaluate: Find θ in [0, 2π) where the polar curve r = sin(2θ) passes through the pole.

Accepted Answer

θ = 0, π/2, π, 3π/2

Answer

r = 0 when sin(2θ) = 0, i.e., 2θ = 0, π, 2π, 3π → θ = 0, π/2, π, 3π/2.

Question 5

Which symmetry does r = 4 + 4 cos θ exhibit?

Accepted Answer

Symmetric about the polar axis

Answer

Replacing θ with −θ leaves the equation unchanged, so it is symmetric about the polar axis.

Trigonometry Practice Test