In a polar coordinate system, we select a point, called the pole, and then a ray with vertex at the pole, called polar axis. A point P in a polar coordinate system is represented by an ordered pair of numbers (r,0). If r>0, then r is the distance of the point from the pole; 0 is an angle formed by the polar axis and a ray from the pole through the point. 0 = 2 3TT P= (r, €) • P= (2, ) 0 = 0 Or=1 r=3 r= 5 Polar axis O Pole 8 = 7T 3TT Polar grid 1. Use table of values and plotting points in polar grid to graph the polar equation 2 Compare your result with results of other members of your group. r = sin 0 2. What type of graph did you get?
In a polar coordinate system, we select a point, called the pole, and then a ray with vertex at the pole, called polar axis. A point P in a polar coordinate system is represented by an ordered pair of numbers (r,0). If r>0, then r is the distance of the point from the pole; 0 is an angle formed by the polar axis and a ray from the pole through the point. 0 = 2 3TT P= (r, €) • P= (2, ) 0 = 0 Or=1 r=3 r= 5 Polar axis O Pole 8 = 7T 3TT Polar grid 1. Use table of values and plotting points in polar grid to graph the polar equation 2 Compare your result with results of other members of your group. r = sin 0 2. What type of graph did you get?
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Transcribed Image Text:In a polar coordinate system, we select a point, called the **pole**, and then a ray with a vertex at the pole, called the **polar axis**. A point \( P \) in a polar coordinate system is represented by an ordered pair of numbers \( (r, \theta) \). If \( r > 0 \), then \( r \) is the distance of the point from the pole; \( \theta \) is an angle formed by the polar axis and a ray from the pole through the point.
### Diagram Explanation
- **Left Diagram**: Shows the basic representation of a polar coordinate system. The point \( P = (r, \theta) \) is located using the distance \( r \) from the pole \( O \) and angle \( \theta \) from the polar axis.
- **Right Diagram**: Depicts a polar grid with points plotted.
- The grid includes several concentric circles with radii marked (e.g., \( r = 1, 3, 5 \)).
- Various angles \( \theta \) (e.g., \( \theta = 0, \frac{\pi}{4}, \frac{\pi}{2}, \pi \)) are indicated along the circular grid.
- Specific points like \( P = (2, \frac{\pi}{4}) \) and \( Q = (4, \frac{5\pi}{4}) \) are highlighted on the grid, showing their positions relative to the pole.
### Exercises
1. Use a table of values and plot points on the polar grid to graph the polar equation \( r = \frac{2}{\sin \theta} \). Compare your result with results of other members of your group.
2. What type of graph did you get?
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