Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
: Let Ra R2 R2 be rotation by a radians counterclockwise. What is the standard matrix of Ro? Prove the addition formulas for cos(a + B) and sin(a + 3) by considering the composite linear map Rẻ ○ Ra.

: Let Ra R2 R2 be rotation by a radians counterclockwise. What is the standard matrix of Ro? Prove the addition formulas for cos(a + B) and sin(a + 3) by considering the composite linear map Rẻ ○ Ra.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Let \( R_{\alpha} : \mathbb{R}^2 \to \mathbb{R}^2 \) be rotation by \( \alpha \) radians counterclockwise. What is the standard matrix of \( R_{\alpha} \)? Prove the addition formulas for \(\cos(\alpha + \beta)\) and \(\sin(\alpha + \beta)\) by considering the composite linear map \( R_{\beta} \circ R_{\alpha} \).
Transcribed Image Text:Let \( R_{\alpha} : \mathbb{R}^2 \to \mathbb{R}^2 \) be rotation by \( \alpha \) radians counterclockwise. What is the standard matrix of \( R_{\alpha} \)? Prove the addition formulas for \(\cos(\alpha + \beta)\) and \(\sin(\alpha + \beta)\) by considering the composite linear map \( R_{\beta} \circ R_{\alpha} \).
Expert Solution
Step 1: Defining the standard matrix

Given Rα:ℝ2→ℝ2

Rα=cosα-sinαsinαcosα

Therefore the standard matrix of Rα is cosα-sinαsinαcosα

 

 

Advanced Math homework question answer, step 1, image 1

 

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
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS