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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