MTH Precalculus | EssayIvy.com

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MTH – Precalculus NAME:

#1 Convert the following rectangular coordinates to polar coordinates…(2 points

each).

The following formula will be used for conversion from

rectangular coordinates (x,y) to polar coordinates (r, θ);

r=√x2+y2

r2=x2+y2

θ=tan−1(y/x)

A) (3,-2)

(√13, 326.310)

B) (-1,1)

(√2, 1350)

C) (-3,-4)

(5, 233.130)

D) (1,3)

(√10,71.570)

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#2 Convert the following polar coordinates to rectangular coordinates….(2 points

each)

The following will be used for conversion

x = r × cos( θ )

y = r × sin( θ )

A) ( 2

) =

(-1, √3)

B) (  

) =

󰇛



󰇜

C) (4, π) =

(-4, 0)

D) (5, 3.2) =

(5, 0.3)

#3 – Rewrite the following equations in rectangular form (3 points each)

A) r cos2 Ө = sin Ө

Divide both sides by cos2 Ө and simplify

R= sin Ө / cos2 Ө

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Ө ≠ π/2 + 2 π n, Ө ≠ 3π/2 + 2 π n

B) r = 4cos (Ө) + 4sin (Ө)

Define the domain=     

The point of intercept on the axis for 4cos (Ө) + 4sin (Ө) = ( 0,4)

5 – Rewrite the following equations in polar form (3 points each)

x = r × cos( θ )

y = r × sin( θ )

Replace these equations in the problem

60x y y  

(r × cos ( θ ))2 + (r × sin( θ ))2 +6 (r × sin( θ ))=0

r2 cos2(θ) + r2 sin2(θ) + 6 r sin (θ)= 0

2 2 2 2

()x x y y

(r × cos ( θ ))2 ((r × cos ( θ ))2+ (r × sin ( θ ))2)= (r × sin ( θ ))2

r2 cos2(θ)(( r2 cos2(θ) + (r2 sin2(θ))= r2 sin2 (θ)

(( r4 cos4(θ) + (r4 cos2(θ) sin2(θ))= r2 sin2 (θ)

3- Use the vectors below to answer the following questions (3 points each)

5, 2v  

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2, 1w  

a) Find the magnitude of

|W|= √(22+-12)

|W|= √5

b) Find

2vw

= (5,-2)+ 2(2,-1)

= (9, -4)

c) Find the unit vector for

|v|=󰇛 󰇜 √29

=󰇛󰇜

 = (󰇛󰇜

, 󰇛󰇜

 󰇜

#4 Graph the following polar curve. Make sure to list all points that are graphed

and be accurate as possible in graphing all points (9 points)

1 2cosr





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The co-ordinates can be obtained from a graphing calculator which

represents the following Cartesian co-ordinates.

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 



  

 



  

 

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#5 – Write the following complex numbers in polar form (2 points each)

A) 3+5i

(5.8, 59.060)

B) -2+4i

(4.5, 116.5650)

C) 2 – 6i

(6.3, 71.5650)

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D) -4- i

(4.1, 165.9640)

#6 – Write the following as complex number in the form

A Bi

Write all answers

with exact values when possible (2 points each)

cis









z = a + b i

a=r cos Ө

b=r sin Ө

z= r cos Ө + (r sin Ө)i

    

  



   

  



         

     

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cis









   

  



          

     

 

6 120cis

    

          

     

 

50cis

    

      

#7 – Find the product

zz

and express the result in rectangular form. Write your

answers with exact values when possible (3 points each)

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2 (100 )

5 (50 )

z cis



Apply the rule a0=1, a≠ 0

1000=1, 500=1

󰇛󰇜 󰇛󰇜 󰇛󰇜 󰇛󰇜

3 (130 )

2 (170 )

z cis



Apply the rule a0=1, a≠ 0

1300=1, 1700=1

󰇛󰇜 󰇛󰇜 󰇛󰇜 󰇛󰇜 

#8 – Find the quotient

and express the result in rectangular form. Write your

answers with exact values when possible (3 points each)

12 (350 )

3 (80 )

z cis



Apply the rule a0=1, a≠ 0

800=1, 3500=1

󰇛󰇜

󰇛󰇜󰇛󰇜

󰇛󰇜 

 

 

 

  

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8 (80 )

2 (35 )

z cis



Apply the rule a0=1, a≠ 0

800=1, 350=1

󰇛󰇜

󰇛󰇜󰇛󰇜

󰇛󰇜 

 

 

 

 

#9 – Evaluate the following and write your answer in rectangular form. Write all

values as exact values when possible (3 points each)

( 3 )i

(a-b)3= a3-3a2b +3ab2-b3

=3√3- 3x3i +3√3 i2-i3

Simplify= -8i

( 3 3 )i

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

 󰇛  󰇜󰇛󰇜󰇛󰇜

 󰇛  󰇜󰇛󰇜󰇛󰇜

 󰇛  󰇜󰇛󰇜󰇛󰇜



 󰇛  󰇜󰇛󰇜󰇛󰇜 

 󰇛  󰇜󰇛󰇜󰇛󰇜



 󰇛  󰇜󰇛󰇜󰇛󰇜

 󰇛  󰇜󰇛󰇜󰇛󰇜



 󰇛  󰇜󰇛󰇜󰇛󰇜

 󰇛  󰇜󰇛󰇜󰇛󰇜



 󰇛  󰇜󰇛󰇜󰇛󰇜

󰇛 󰇜󰇛󰇜󰇛󰇜

= - 1889568i

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