Precalc CH 9

Find the polar coordinates that do not describe the point in the given graph. A (-2, 30°) B (-2, 210°) C (2, 30°) D (-2, -150°)

A

ROBOT A robot's hand is positioned so its center has polar coordinates (3, 180°). Find rectangular coordinates for this point. A (-3, 0) B (0, 3) C (3, 0) D (0, -3)

A

AIRPLANES Two airplanes at the same altitude have polar coordinates (2, 120°) and (1, 45°), where r is in miles. Find the distance between them. A 1.40 miles B 1.99 miles C 2.46 miles D 2.98 miles

B

Let z1 = 4(cos 135˚ + i sin 135˚) and z2 = 2(cos 45˚ + i sin 45˚). Write the rectangular form of z1z2. A -8i B -8 C 8 + 8i D 8

B

9. Write the polar equation r = 3 in rectangular form. A x^2 - 9 = 0 B x^2 + y^2 - 9y = 0 C x^2 + y^2 = 9 D xy = 9

C

Find the directrix for the polar equation r = 10/1 + 2 cos θ A x = 1 B y = 2 C x = 5 D y = 10

C

PHYSICS The force on an object is represented by the complex number 5 + 18i. The magnitude of the force is measured in pounds and is equal to the absolute value of the number. Find the magnitude of the force on the object. A 15.5 lb B 17.3 lb C 18.7 lb D 74.5 lb

C

Express 3 √3 + 3i in polar form. A 3 (cos π/6+ i sin π/6) B 6 (cos π/6- i sin π/6) C 6 (cos π/3+ i sin π/3) D 6 (cos π/6+ i sin π/6)

D

Let z1 = 4(cos 135˚ + i sin 135˚) and z2 = 2(cos 45˚ + i sin 45˚). Write the rectangular form of Simplify ( √3 + i) 4 and express the result in rectangular form. A 8 + 8 √3 i B 8 - 8 √3 i C 16 + 16 √3 i D -8 + 8 √3 i

D

Let z1 = 4(cos 135˚ + i sin 135˚) and z2 = 2(cos 45˚ + i sin 45˚). Write the rectangular form of Write the rectangular form of z1/z 2 F 2i G -2 H -2i J 2 + 2i

F

Write a polar equation for the conic with eccentricity 2 and directrix y = 4. F r = 8/1 + 2 sin θ H r = 4/1 - 2 sin θ G r = 8/1 + 2 cos θ J r = 4/1 - 2 cos θ

F

Express 2 (cos π/3+ i sin π/3) in rectangular form. F -1 + √3 i G 1 + √3 i H 1 - √3 i J √3 + i

G

Find polar coordinates for the point with rectangular coordinates ( √3 , 1) if 0 ≤ θ ≤ 2π and r ≥ 0. F (2, π/ 3) G (2, π/6) H (2, π/ 4) J (1, π/ 6)

G

SHIP A ship is approaching a port on the curve of a conic described by the equation r = 12/1 + 20 cos θ Find the type of conic for the equation. F ellipse H parabola that opens downward G hyperbola J parabola that opens upward

G

Find a cube root of i. F √3/2 - 1/2i G -√3/2 - 1/2i H √3/2 + 1/2i J 1/2 + √3/2i

H

Find the eccentricity of the polar equation r = 5 /1 + 3 sin θ. F 1 G 2 H 3 J 5

H

Find the equation which is graphed at the right. F r = 4 cos θ G r = 2 - 2 cos θ H r = 2 + 2 cos θ J r = 2 + 2 sin θ

H

Find the equation represented in the given graph. F θ = 3 G r = 3 H θ = 2π J r = 2

J

Write the rectangular equation x = 3 in polar form. F r = 3 csc θ G r = 3 H θ = 3 J r = 3 sec θ

J

Identify the graph for the polar equation r = 4 sin θ.

perfect circle C