Solution Found!
a. Calculate AA and AA . (Recall the definition of the rotation matrix on p. 98.) b. Use
Chapter 2, Problem 7(choose chapter or problem)
a. Calculate \(A_\theta A_\phi\) and \(A_\phi A_\theta\). (Recall the definition of the rotation matrix on p. 98.)
b. Use your answer to part a to derive the addition formulas for sine and cosine.
Questions & Answers
(3 Reviews)
QUESTION:
a. Calculate \(A_\theta A_\phi\) and \(A_\phi A_\theta\). (Recall the definition of the rotation matrix on p. 98.)
b. Use your answer to part a to derive the addition formulas for sine and cosine.
ANSWER:Step 1 of 3
The rotation matrix is given to find the product of two matrices with different angles.
The rotation matrix is:
\({A_\theta } = \left[ {\begin{array}{*{20}{c}}{\cos \theta }&{ - \sin \theta }\\{\sin \theta }&{\cos \theta }\end{array}} \right]\)
The other matrix is:
\({A_\phi } = \left[ {\begin{array}{*{20}{c}}{\cos \phi }&{ - \sin \phi }\\{\sin \phi }&{\cos \phi }\end{array}} \right] \)
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Review this written solution for 964553) viewed: 164 isbn: 9781429215213 | Linear Algebra: A Geometric Approach - 2 Edition - Chapter 2.2 - Problem 7
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Review this written solution for 964553) viewed: 164 isbn: 9781429215213 | Linear Algebra: A Geometric Approach - 2 Edition - Chapter 2.2 - Problem 7
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Review this written solution for 964553) viewed: 164 isbn: 9781429215213 | Linear Algebra: A Geometric Approach - 2 Edition - Chapter 2.2 - Problem 7
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