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For Exercises 15-18, plot the points whose polar coordinates are given. (See Example Label each point a, b, c, d! (4) (a5.) 16. a. 3, 11T b. (4.5, c. 6. a (-2) d.

For Exercises 15-18, plot the points whose polar coordinates are given. (See Example Label each point a, b, c, d! (4) (a5.) 16. a. 3, 11T b. (4.5, c. 6. a (-2) d.

Trigonometry (11th Edition)
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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For exercises 15-18, plot the points whose polar coordinates are given. Label each point a,b,c,d
This image displays a polar coordinate graph commonly used in mathematics and physics to represent complex functions and directional data. ### Description: 1. **Concentric Circles**: - The graph consists of concentric circles centered at the origin. - Each circle represents a constant radius value, increasing by units of 1. The innermost circle is labeled as 1, and the values increase outwardly, ending at 10. 2. **Radial Lines**: - Lines radiate outward from the center, dividing the graph into equal angular sections. - These lines likely represent angles, typically measured in degrees or radians. 3. **Axes**: - There are two perpendicular axes intersecting at the center, typically representing the horizontal and vertical directions. - The axes are marked with positive and negative values, indicating directionality. Each direction extends to the value of 10, both positive and negative. ### Application: This type of graph is valuable for: - **Trigonometric Functions**: Visualizing sine and cosine waves over a circular framework. - **Navigation and Robotics**: Indicating directions relative to a central point. - **Data Representation**: Displaying multivariate data in fields like meteorology or data science. Understanding polar graphs is essential for interpreting and representing data points in circular formats, facilitating analysis in various scientific and engineering disciplines.
Transcribed Image Text:This image displays a polar coordinate graph commonly used in mathematics and physics to represent complex functions and directional data. ### Description: 1. **Concentric Circles**: - The graph consists of concentric circles centered at the origin. - Each circle represents a constant radius value, increasing by units of 1. The innermost circle is labeled as 1, and the values increase outwardly, ending at 10. 2. **Radial Lines**: - Lines radiate outward from the center, dividing the graph into equal angular sections. - These lines likely represent angles, typically measured in degrees or radians. 3. **Axes**: - There are two perpendicular axes intersecting at the center, typically representing the horizontal and vertical directions. - The axes are marked with positive and negative values, indicating directionality. Each direction extends to the value of 10, both positive and negative. ### Application: This type of graph is valuable for: - **Trigonometric Functions**: Visualizing sine and cosine waves over a circular framework. - **Navigation and Robotics**: Indicating directions relative to a central point. - **Data Representation**: Displaying multivariate data in fields like meteorology or data science. Understanding polar graphs is essential for interpreting and representing data points in circular formats, facilitating analysis in various scientific and engineering disciplines.
**For Exercises 15–18, plot the points whose polar coordinates are given. (See Example 1)** **Label each point a, b, c, d!** **16.** a. \( \left( 3, \frac{\pi}{3} \right) \) b. \( \left( 4.5, \frac{11\pi}{4} \right) \) c. \( \left( -5, \frac{5\pi}{6} \right) \) d. \( \left( -3, \frac{\pi}{4} \right) \) **18.** a. \( \left( 2, \frac{2\pi}{3} \right) \) b. \( (3, -\pi) \) c. \( \left( -4, -\frac{\pi}{4} \right) \) d. \( \left( -5, -\frac{5\pi}{6} \right) \) **Graph Description:** Two polar grids are provided to plot the given points. Each grid has concentric circles and radial lines indicating angles. The circles represent distances from the center (polar origin), while the radial lines are spaced according to common angle increments. The task involves placing each point based on its radial distance and angular position.
Transcribed Image Text:**For Exercises 15–18, plot the points whose polar coordinates are given. (See Example 1)** **Label each point a, b, c, d!** **16.** a. \( \left( 3, \frac{\pi}{3} \right) \) b. \( \left( 4.5, \frac{11\pi}{4} \right) \) c. \( \left( -5, \frac{5\pi}{6} \right) \) d. \( \left( -3, \frac{\pi}{4} \right) \) **18.** a. \( \left( 2, \frac{2\pi}{3} \right) \) b. \( (3, -\pi) \) c. \( \left( -4, -\frac{\pi}{4} \right) \) d. \( \left( -5, -\frac{5\pi}{6} \right) \) **Graph Description:** Two polar grids are provided to plot the given points. Each grid has concentric circles and radial lines indicating angles. The circles represent distances from the center (polar origin), while the radial lines are spaced according to common angle increments. The task involves placing each point based on its radial distance and angular position.
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