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Note: The equation for the Unit Circle is x² + y² = 1. Recall from Math141 (Precalculus I): When both (-x, y) and (x, y) are on a graph, you have y-axis symmetry. When both (x, y) and (x, y) are on a graph, you have x-axis symmetry. When both (-x, -y) and (x, y) are on a graph, you have symmetry about the origin (BOTH axes). 1. Use the equation for the Unit Circle to show that circles centered at the origin are symmetric about the x-axis, y-axis, and the origin. (In other words, perform the tests for symmetry.) One test will be completed for you: y-axis symmetry test: (-x)² + y² = 1 x² + y² = 1 Since we replaced x with -x and then, arrived at the same Unit Circle Equation, then (x,y) and (-x,y) are on the circle, showing y-axis symmetry. Now, show the other two tests of symmetries. x-axis symmetry test: 2 x² + (y) ³² = 1 22=1 x²-y origin symmetry test:

Note: The equation for the Unit Circle is x² + y² = 1. Recall from Math141 (Precalculus I): When both (-x, y) and (x, y) are on a graph, you have y-axis symmetry. When both (x, y) and (x, y) are on a graph, you have x-axis symmetry. When both (-x, -y) and (x, y) are on a graph, you have symmetry about the origin (BOTH axes). 1. Use the equation for the Unit Circle to show that circles centered at the origin are symmetric about the x-axis, y-axis, and the origin. (In other words, perform the tests for symmetry.) One test will be completed for you: y-axis symmetry test: (-x)² + y² = 1 x² + y² = 1 Since we replaced x with -x and then, arrived at the same Unit Circle Equation, then (x,y) and (-x,y) are on the circle, showing y-axis symmetry. Now, show the other two tests of symmetries. x-axis symmetry test: 2 x² + (y) ³² = 1 22=1 x²-y origin symmetry test:

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Activity 4. Finding the x- and y- coordinates for each of the angles on Circle A and Circle B in Quadrants II, III, and IV. Note: The equation for the Unit Circle is x² + y2 = 1. Recall from Math141 (Precalculus I): When both (-x, y) and (x, y) are on a graph, you have y-axis symmetry. When both (x, y) and (x, y) are on a graph, you have x-axis symmetry. When both (-x, -y) and (x, y) are on a graph, you have symmetry about the origin (BOTH axes). 1. Use the equation for the Unit Circle to show that circles centered at the origin are symmetric about the x-axis, y-axis, and the origin. (In other words, perform the tests for symmetry.) One test will be completed for you: y-axis symmetry test: (-x)² + y² = 1 x² + ² = 1 Since we replaced x with -x and then, arrived at the same Unit Circle Equation, then (x,y) and (-x,y) are on the circle, showing y-axis symmetry. Now, show the other two tests of symmetries. x-axis symmetry test: x² + + y)² = 1 -y 2 2=1 x 2. Using y-axis symmetry and the points in Quadrant I, identify below what 3 points would be in Quadrant II on Circles A and B. Label those points accordingly on Circles A and B. Three Points: origin symmetry test: 3. Using x-axis symmetry and the points in Quadrant I, identify below what 3 points would be in Quadrant IV on Circles A and B. Label those points accordingly on Circles A and B. Three Points: 4. Using symmetry about the origin and the points in Quadrant I, identify below what 3 points would be in Quadrant III on Circles A and B. Label those points accordingly on Circles A and B. Three Points: 5
Transcribed Image Text:Activity 4. Finding the x- and y- coordinates for each of the angles on Circle A and Circle B in Quadrants II, III, and IV. Note: The equation for the Unit Circle is x² + y2 = 1. Recall from Math141 (Precalculus I): When both (-x, y) and (x, y) are on a graph, you have y-axis symmetry. When both (x, y) and (x, y) are on a graph, you have x-axis symmetry. When both (-x, -y) and (x, y) are on a graph, you have symmetry about the origin (BOTH axes). 1. Use the equation for the Unit Circle to show that circles centered at the origin are symmetric about the x-axis, y-axis, and the origin. (In other words, perform the tests for symmetry.) One test will be completed for you: y-axis symmetry test: (-x)² + y² = 1 x² + ² = 1 Since we replaced x with -x and then, arrived at the same Unit Circle Equation, then (x,y) and (-x,y) are on the circle, showing y-axis symmetry. Now, show the other two tests of symmetries. x-axis symmetry test: x² + + y)² = 1 -y 2 2=1 x 2. Using y-axis symmetry and the points in Quadrant I, identify below what 3 points would be in Quadrant II on Circles A and B. Label those points accordingly on Circles A and B. Three Points: origin symmetry test: 3. Using x-axis symmetry and the points in Quadrant I, identify below what 3 points would be in Quadrant IV on Circles A and B. Label those points accordingly on Circles A and B. Three Points: 4. Using symmetry about the origin and the points in Quadrant I, identify below what 3 points would be in Quadrant III on Circles A and B. Label those points accordingly on Circles A and B. Three Points: 5
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