Pre-Calculus



Pre-Calculus Name

Chapter 9 – Polar Coordinates and Complex Numbers Period

1. Graph each point.

a. ( 2 , 120º )

b. ( -3 , [pic] )

c. ( 4 , -165º )

d. ( -1 , [pic] )

2. Graph each equation.

a. [pic]

b. [pic]

c. [pic]

d. [pic]

3. Name the four pairs of polar coordinates

for point S.

4. Find the distance between the points. [pic]

a. ( 4 , 170° ) and ( 6 , 105° ) b. ( 1 , [pic] ) and ( 5 , [pic] )

5. A surveyor uses a device called a theodolite to measure angles. While mapping out a level site, a surveyor identifies a landmark 450 feet away and 30º to the left and another landmark 600 feet away and 50º to the right. What is the distance between the landmarks?

A polar graph is the set of all points whose coordinates [pic] satisfy a given polar equation.

For #6 to #8, make a table of values. Round the values of r to the nearest tenth. Graph the ordered pairs and connect them with a smooth curve.

6. r = 3sin [pic]

7. [pic]

8. [pic]

9. Solve the system of equations using algebra and trigonometry. Verify using your calculator.

a) [pic]

b) [pic]

Pre-Calculus Name

Chapter 9 – Polar Coordinates and Complex Numbers Period

For #1 to #3, make a table of values. Round the values of r to the nearest tenth. Graph the ordered pairs and connect them with a smooth curve.

1. r = 2.5+2.5cos [pic]

2. [pic]

3. r = 1 − 2sin [pic]

Make a quick sketch of how you think the graph will look like. Check using your calculator

4. [pic] 5. [pic] 6. [pic]

7. [pic] 8. [pic] 9. [pic]

10. [pic] 11. [pic] 12. [pic]

Pre-Calculus Name

Chapter 9 – Polar Coordinates and Complex Numbers Period

1. Find the polar coordinates of the point with the given rectangular coordinates.

a. ( -5 , 12 ) b. ( 3 , -3 ) c. ( -2 , [pic] )

2. Find the rectangular coordinates of the point with polar coordinates.

a. [pic] b. [pic] c. [pic]

3. Write the rectangular equations in polar form.

a. [pic] b. [pic] c. [pic]

4. Write the polar equations in rectangular form.

a. [pic] b. [pic] c. [pic]

Pre-Calculus Name

Chapter 9 – Polar Coordinates and Complex Numbers Period

Simplify each complex expression.

1. [pic] 2. [pic]

3. [pic] 4. [pic]

5. [pic]

Pre-Calculus Name

Chapter 9 – Polar Coordinates and Complex Numbers Period

1. Express in polar form. (exact)

a) [pic]

b) [pic]

2. Express in rectangular form. (exact)

a) [pic] b) [pic]

3. Solve the equation for x and y , where x and y are real numbers.

[pic]

Make a quick sketch of how you think the graph will look like. Check using your calculator

4. [pic] 5. [pic] 6. [pic]

7. [pic] 8. [pic] 9. [pic]

10. [pic] 11. [pic] 12. [pic]

Pre-Calculus Name

Chapter 9 – Polar Coordinates and Complex Numbers Period

Find each product or quotient and write each answer in exact rectangular form , [pic] .

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. Find the impedance in a circuit with a voltage of 100 volts and a current of [pic] amps.

[ Use the Real World Application problem on p593 and Example 3 on p595 as a hint. ]

Pre-Calculus Name

Chapter 9 – Polar Coordinates and Complex Numbers Period

Find each power. Write your answer in exact rectangular form.

1. [pic] 2. [pic]

3. [pic]

Find each principal root. Write your answer in exact rectangular form.

4. [pic] 5. [pic]

6. Find the fourth roots of [pic].

Solve for ALL ROOTS of each equation. Write your answer in exact rectangular form.

7. [pic] 8. [pic]

-----------------------

9.1 and 9.2 Supplementary Worksheet

[pic]

[pic]

[pic]

S

[pic]

|[pic] |3[pic] |[pic] |

|0 | | |

|À/6 | | |

|À/4 | | |

|À/3 | | |

|À/2 | | |

|2À/3 | | |

|3À/4 | | |

|5À/6 | | |

|À | | |

|7À/6 | | |

|5À/4 | | |

|4À/3 | | |

|3À/2 | | |

|5À/3 | | |

|7À/4 | | |

|11À/6 | | |

[pic]

|[pic] |[pic] |[pic] |

|0 | | |

|π/6 | | |

|π/4 | | |

|π/3 | | |

|π/2 | | |

|2π/3 | | |

|3π/4 | | |

|5π/6 | | |

|π | | |

|7π/6 | | |

|5π/4 | | |

|4π/3 | | |

|3π/2 | | |

|5π/3 | | |

|7π/4 | | |

|11π/6 | | |

[pic]

|[pic] |[pic] |[pic] |

|0 | | |

|π/6 | | |

|π/4 | | |

|π/3 | | |

|π/2 | | |

|2π/3 | | |

|3π/4 | | |

|5π/6 | | |

|π | | |

|7π/6 | | |

|5π/4 | | |

|4π/3 | | |

|3π/2 | | |

|5π/3 | | |

|7π/4 | | |

|11π/6 | | |

9.2 Supplementary Worksheet

[pic]

|[pic] |2.5+2.5cos [pic] |[pic] |

|0 | | |

|π/6 | | |

|π/4 | | |

|π/3 | | |

|π/2 | | |

|2π/3 | | |

|3π/4 | | |

|5π/6 | | |

|π | | |

|7π/6 | | |

|5π/4 | | |

|4π/3 | | |

|3π/2 | | |

|5π/3 | | |

|7π/4 | | |

|11π/6 | | |

[pic]

|[pic] |[pic] |[pic] |

|0 | | |

|π/6 | | |

|π/4 | | |

|π/3 | | |

|π/2 | | |

|2π/3 | | |

|3π/4 | | |

|5π/6 | | |

|π | | |

|7π/6 | | |

|5π/4 | | |

|4π/3 | | |

|3π/2 | | |

|5π/3 | | |

|7π/4 | | |

|11π/6 | | |

[pic]

|[pic] |1 − 2sin [pic] |[pic] |

|0 | | |

|π/6 | | |

|π/4 | | |

|π/3 | | |

|π/2 | | |

|2π/3 | | |

|3π/4 | | |

|5π/6 | | |

|π | | |

|7π/6 | | |

|5π/4 | | |

|4π/3 | | |

|3π/2 | | |

|5π/3 | | |

|7π/4 | | |

|11π/6 | | |

9.3 Supplementary Worksheet

9.5 Supplementary Worksheet

Conversion Formula: [pic]

9.6 Supplementary Worksheet

[pic]

9.7 Supplementary Worksheet

9.8 Supplementary Worksheet

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