Homework Help is Here – Start Your Trial Now!
Math
Algebra
y X 0 A Which ordered pair represents the coordinates of point P? A (-sin 0, -cos 0) B (-cos 0, -sin 0) C (-sin(0), cos(0 - π)) D (-cos(0-1), sin(0 - ))

y X 0 A Which ordered pair represents the coordinates of point P? A (-sin 0, -cos 0) B (-cos 0, -sin 0) C (-sin(0), cos(0 - π)) D (-cos(0-1), sin(0 - ))

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,...
See similar textbooks
icon
Related questions
Question
### Coordinate Plane Illustration and Trigonometric Analysis **Diagram Description:** The diagram shows a circle centered at the origin of a coordinate plane with radius \(1\). The circle is intersected by the \(x\)-axis and \(y\)-axis at points \((1, 0)\), \((-1, 0)\), \((0, 1)\), and \((0, -1)\). There is an angle \(\theta\) drawn from the positive \(x\)-axis counterclockwise to a point \(A\) on the circumference of the circle in the first quadrant. An additional line segment extends from \(A\) to point \(P\) on the circumference of the circle in the third quadrant (making an angle \(\theta\) in the third quadrant). **Choices for Ordered Pair Coordinates of Point \(P\):** Which ordered pair represents the coordinates of point \(P\)? - **A)** \((- \sin \theta, - \cos \theta)\) - **B)** \((- \cos \theta, - \sin \theta)\) - **C)** \((- \sin (\theta - \pi), - \cos (\theta - \pi))\) - **D)** \((- \cos (\theta - \pi), - \sin (\theta - \pi))\) The correct answer is **highlighted in yellow**. ### Explanation: Analyze the geometry and trigonometry: 1. **Point \(A\) Coordinates**: - From the unit circle, \(A\) at angle \(\theta\) has coordinates \((\cos \theta, \sin \theta)\). 2. **Symmetric Point \(P\)**: - To find \(P\) in the third quadrant (opposite \(A\)), phase shift by \(\pi\) radians. - Coordinates of \(P\): \(P = A + \pi\), which becomes \((\cos (\theta + \pi), \sin (\theta + \pi))\). - Using trigonometric identities: - \(\cos (\theta + \pi) = -\cos \theta\) - \(\sin (\theta + \pi) = -\sin \theta\) Thus, the coordinates of \(P\) are \((- \cos \theta, - \sin \theta)\). However, the corresponding multiple-choice option
Transcribed Image Text:### Coordinate Plane Illustration and Trigonometric Analysis **Diagram Description:** The diagram shows a circle centered at the origin of a coordinate plane with radius \(1\). The circle is intersected by the \(x\)-axis and \(y\)-axis at points \((1, 0)\), \((-1, 0)\), \((0, 1)\), and \((0, -1)\). There is an angle \(\theta\) drawn from the positive \(x\)-axis counterclockwise to a point \(A\) on the circumference of the circle in the first quadrant. An additional line segment extends from \(A\) to point \(P\) on the circumference of the circle in the third quadrant (making an angle \(\theta\) in the third quadrant). **Choices for Ordered Pair Coordinates of Point \(P\):** Which ordered pair represents the coordinates of point \(P\)? - **A)** \((- \sin \theta, - \cos \theta)\) - **B)** \((- \cos \theta, - \sin \theta)\) - **C)** \((- \sin (\theta - \pi), - \cos (\theta - \pi))\) - **D)** \((- \cos (\theta - \pi), - \sin (\theta - \pi))\) The correct answer is **highlighted in yellow**. ### Explanation: Analyze the geometry and trigonometry: 1. **Point \(A\) Coordinates**: - From the unit circle, \(A\) at angle \(\theta\) has coordinates \((\cos \theta, \sin \theta)\). 2. **Symmetric Point \(P\)**: - To find \(P\) in the third quadrant (opposite \(A\)), phase shift by \(\pi\) radians. - Coordinates of \(P\): \(P = A + \pi\), which becomes \((\cos (\theta + \pi), \sin (\theta + \pi))\). - Using trigonometric identities: - \(\cos (\theta + \pi) = -\cos \theta\) - \(\sin (\theta + \pi) = -\sin \theta\) Thus, the coordinates of \(P\) are \((- \cos \theta, - \sin \theta)\). However, the corresponding multiple-choice option
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS