Polar Coordinates Test

Which of the following points lies on the graph of r = 2 - 3cosθ?

(-1, 0°)

Convert the polar coordinates (2, 3π) to Cartesian coordinates.

(-2, 0)

Convert the Cartesian coordinates (1, -√3) to polar coordinates.

(2, 300°)

Find z1×z2 for z1 = 9(cos⁡225∘+isin⁡225∘) and z2 = 3(cos⁡45∘+isin⁡45∘). Express the product in a+bi form.

-27i

Express 2(cos150° + isin150°) in a + bi form.

-√3 + i

Which of the following is an argument of one of the fourth roots of 16(cos80° + isin80°)?

20°

The modulus of (1 + 2i)^4 is _____.

25

If z = √5 + √3i, then |z| = _____.

2√2

What is the argument of 3 - 3i?

315°

Find z1/z2 if z1 = 8√3(cos180° + isin180°) and z2 = 2√3(cos60° + isin60°).

4(cos120° + isin120°)

Write the equation of the conic satisfying the given conditions. focus at the pole, e = 3/4, directrix rsinθ = -2

6/4-3sinθ

Graph the point having the polar coordinates (- 4, 180°).

https://ibb.co/6B7fVkw

Choose the graph of the polar equation r = -sinθ.

https://ibb.co/V9gHGTX

Graph the point having the polar coordinates (3, -150°).

https://ibb.co/j3VWvmV

Choose the graph of the polar equation r = 3.

https://ibb.co/s1dtBKF

Identify the conic whose equation is given. r = 2/3+5sinθ

hyperbola

Convert the Cartesian equation x² + y² - 2x = 0 to a polar equation.

r = 2cosθ

A conic section whose focus is at the pole has the equation r = 2/1+cosθ. Which of the following equations is the directrix of the conic?

rcosθ = 2

Convert the Cartesian equation 2xy = 1 to a polar equation.

r²sin2θ = 1

Which of the following describes the graph of the polar equation rcosθ = 4?

vertical line through 4