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1. On the polar coordinate grid shown below, graph the following points (given in polar coordinates). It’s important to NOTE that, even though the grids shown below look different from the Cartesian coordinate grids you graphed on in high school, what you are graphing in is still the same plane you graphed in then, and any point you graph always has both a set of rectangular coordinates and a set (rather, many sets) of polar coordinates. The grid is just an additional structure that helps us graph things. (a) (5, 30°) (b) (2, 11/6π) (c) (3, − 270°) (d) ( − 6, 1/4 π) 2. For each point graphed in the previous problem, give a different possible set of polar coordinates for the same point. For each point, give a pair of coordinates with a nonnegative radius and a different angle measure from the one given (not just the same angle measure expressed in degrees/radians).

1. On the polar coordinate grid shown below, graph the following points (given in polar coordinates). It’s important to NOTE that, even though the grids shown below look different from the Cartesian coordinate grids you graphed on in high school, what you are graphing in is still the same plane you graphed in then, and any point you graph always has both a set of rectangular coordinates and a set (rather, many sets) of polar coordinates. The grid is just an additional structure that helps us graph things. (a) (5, 30°) (b) (2, 11/6π) (c) (3, − 270°) (d) ( − 6, 1/4 π) 2. For each point graphed in the previous problem, give a different possible set of polar coordinates for the same point. For each point, give a pair of coordinates with a nonnegative radius and a different angle measure from the one given (not just the same angle measure expressed in degrees/radians).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. On the polar coordinate grid shown below, graph the following points (given in polar coordinates). It’s important to NOTE that, even though the grids shown below look different from the Cartesian coordinate grids you graphed on in high school, what you are graphing in is still the same plane you graphed in then, and any point you graph always has both a set of rectangular coordinates and a set (rather, many sets) of polar coordinates. The grid is just an additional structure that helps us graph things. (a) (5, 30°) (b) (2, 11/6π) (c) (3, − 270°) (d) ( − 6, 1/4 π) 2. For each point graphed in the previous problem, give a different possible set of polar coordinates for the same point. For each point, give a pair of coordinates with a nonnegative radius and a different angle measure from the one given (not just the same angle measure expressed in degrees/radians).
# MAT 1093 – Precalculus ## Practice Mathematics Writing Assignment – Module 11 In class, we talked about how the *rectangular coordinates* (x, y) of a point give the signed distances of that point from the vertical and horizontal axes (that is, the signed horizontal and vertical distances from the origin), while the *polar coordinates* (r, θ) give the distance of the point from the origin and the bearing (or direction) of the point, measured as a counterclockwise angle from the positive x-axis (also commonly called the *polar axis*). In this activity, we'll practice graphing points given their polar coordinates, translating between rectangular and polar coordinates, and analyzing basic equations in polar coordinates. 1. **On the polar coordinate grid shown below, graph the following points (given in polar coordinates).** *It's important to NOTE that, even though the grids shown below look different from the Cartesian coordinate grids you graphed on in high school, what you are graphing in is still the same plane you graphed in then, and any point you graph always has both a set of rectangular coordinates and a set (rather, many sets) of polar coordinates. The grid is just an additional structure that helps us graph things.* (a) (5, 30°) (−6, \( \frac{1}{4} \pi \)) (b) (2, \( \frac{11}{6} \pi \)) (c) (3, −270°) (d) ![Polar Coordinate Grid](https://via.placeholder.com/300) The diagram is a polar coordinate grid with concentric circles and radial lines marking angles from 0° to 360° in increments of 15°. 2. **For each point graphed in the previous problem, give a different possible set of polar coordinates for the same point. For each point, give a pair of coordinates with a nonnegative radius and a different angle measure from the one given (not just the same angle measure expressed in degrees/radians).**
Transcribed Image Text:# MAT 1093 – Precalculus ## Practice Mathematics Writing Assignment – Module 11 In class, we talked about how the *rectangular coordinates* (x, y) of a point give the signed distances of that point from the vertical and horizontal axes (that is, the signed horizontal and vertical distances from the origin), while the *polar coordinates* (r, θ) give the distance of the point from the origin and the bearing (or direction) of the point, measured as a counterclockwise angle from the positive x-axis (also commonly called the *polar axis*). In this activity, we'll practice graphing points given their polar coordinates, translating between rectangular and polar coordinates, and analyzing basic equations in polar coordinates. 1. **On the polar coordinate grid shown below, graph the following points (given in polar coordinates).** *It's important to NOTE that, even though the grids shown below look different from the Cartesian coordinate grids you graphed on in high school, what you are graphing in is still the same plane you graphed in then, and any point you graph always has both a set of rectangular coordinates and a set (rather, many sets) of polar coordinates. The grid is just an additional structure that helps us graph things.* (a) (5, 30°) (−6, \( \frac{1}{4} \pi \)) (b) (2, \( \frac{11}{6} \pi \)) (c) (3, −270°) (d) ![Polar Coordinate Grid](https://via.placeholder.com/300) The diagram is a polar coordinate grid with concentric circles and radial lines marking angles from 0° to 360° in increments of 15°. 2. **For each point graphed in the previous problem, give a different possible set of polar coordinates for the same point. For each point, give a pair of coordinates with a nonnegative radius and a different angle measure from the one given (not just the same angle measure expressed in degrees/radians).**
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