precalc homework 10

Math 121 – Homework 10 – Due Tuesday, December 4

1. Plot and label the points on the polar graph:

2. Convert the following points from polar form to rectangular form.

a.

b.

c.

P 5, 3π 4

⎛ ⎝⎜

⎞ ⎠⎟ , Q −3,

π 6

⎛ ⎝⎜

⎞ ⎠⎟ , R 4,

23π 6

⎛ ⎝⎜

⎞ ⎠⎟ .

P 10, π 6

⎛ ⎝⎜

⎞ ⎠⎟

Q 5, 3π 2

⎛ ⎝⎜

⎞ ⎠⎟

R −4, 2π 3

⎛ ⎝⎜

⎞ ⎠⎟

3. Convert the following points from rectangular form to polar form. a.

b.

c.

4. Convert the following equations from rectangular form to polar form. a.

b.

c.

5. Convert the following equations from polar form to rectangular form.

a.

b.

c.

A −2 3,2( )

B −7,−7( )

C 0,−9( )

y = 2

x−4( )2 + y2 =16

y = 3x

r = 6sinθ

r = 5cscθ

θ = −π 4

6. Given the polar equation Complete the following table and graph the

curve.

r = 4−4cosθ.

θ r

0 π /3 π / 2 2π /3 π 4π /3 3π / 2 5π /3 2π

7. Convert the following complex numbers to form

a.

b.

8. Let and .

a. Express in form.

b. Express in form.

r cosθ + isinθ( ) z1 = 5−5i

z2 = −4−4 3i

z1 = 7 cos140 o + isin140o( ) z2 = 5 cos130o + isin130o( ) z1z2 r cosθ + isinθ( )

z1z2 x+ yi

9. Let and .

a. Express in form.

b. Express in form.

10. Use form to evaluate the following. Express the solutions in form.

a.

b.

z1 =12 cos100 o + isin100o( ) z2 = 6 cos40o + isin40o( )

z1 z2

r cosθ + isinθ( )

z1 z2

x+ yi

r cosθ + isinθ( ) x+ yi

2 cos20o + isin20o( )⎡⎣ ⎤⎦ 6

2+2i( )3