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.### Exercises1. 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?

First we will plot some points on the polar grid by taking some suitable values of angle and then…

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°.

See similar textbooks

Related questions

Q: Decide if the points given in polar coordinates are the same. If they are the same, enter T. If they…

A: A)6, π3 (quadrant-1)-6,-π3 -6 cosπ3, 6 sinπ3(quadrant-2)B)2, 35π4=2, 3π4 (quadrant-2)2, -35π42…

Q: Simplify: x6.y2.z3 3) x4.y4.z2 4) — (х3)0

A: Given that: 3. x6.y2.z3x4.y4.z24.-(x3)0

Q: Plot the points from the table below on the polar grid that follows.

A: Plot the points from the table below on the polar grid that follows.Explanation:To plot a point in…

Q: Let = 3 - 4 - 6 K, and = -2 +2 - 2k, Calculate , ull, lv • ull, and e (the angle between and in…

Q: Convert the Cartesian coordinates below to polar coordinates. Give an angle in the range 0 0. (- A.…

A: NOTE: Refresh your page if you can't see any equations. . the given cartesian coordinate is the…

Q: The Cartesian coordinates of the polar coordinates (7, 65°) is.... Select one: a. (6.34, 2.96) b.…

A: Given the polar coordinates is 7,65° The formula is, r=x2+y2θ=tan-1yx Given that r=7,θ=65

Q: sin (- ): %3D 4 II

A: Since you have asked multiple questions in single request so we will be answering only first…

Q: The Cartesian coordinates of a point is (4, -4√3). This point in polar coordinates can be…

Q: Two points are specified using polar coordinates. Find the distance between the points. 10) (4,…

A: Convert polar coordinates r,θ to Cartesian coordinates x,y using below result : x=r cos θ y=r sin θ…

Q: A(4, ST) (+2) 5л 6. A(- 3, 4) a) b)

Q: The point specified by the polar coordinates (7.00, 35.0°) is following when converted to Cartesian…

A: Calculating the cos and sin theta cos(35o) = 0.81915sin(35o) =0.5736

Q: Given point Q=(-8√2,8√2) i in rectangular coordinates, what are the corresponding pol

Question

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?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

a. For the point with rectangular coordinates (-7,24), give three sets of polar coordiantes, two with positive angle measurements and one with a negative angle measure. Round to two decimal places. b. Give the coordinates, to two decimal places, of the point whose polar coordinates are (6;-115 degrees)
1. Determine the direction cosines and direction angles for Ã =
Which equation is the polar equivalent to the equation y =-z? O 0 = O 0 = O 0 =
Convert the Cartesian coordinate (-2,-1) to polar coordinates, 0≤theta<2pi. round theta to nearest hundreths
Graph the point with the polar coordinates -5,- -3) Give two alternative representations of the point in polar coordinates. Choose the correct graph of the point below. O A. -5 Ay 5 -5- C. π A. 5,6 5x 3 Q Choose the two points below that refer to the same point as DE. -5,6 OB. discrete Structur....pdf -5 Ay -5,- discrete Structur....pdf WIH Q O C. -5 B. F. 5x -5, 2π Q D.
5. The Cartesian coordinates of the polar coordinates (8, -107 °) is ... a. (-2.34, -7.65) b. (-7.65, -2.34) c. (7.86, -1.48)