tation by an angle 0 can be written in matrix form as: [cos(0) - sin(0)] sin(0) cos(0) Use this and composition of linear transformations to show the following trigonometric io cos(0, + 02) = cos(01) cos(02) – sin(61) sin(02) sin(61 + 02) = sin(81) cos(02) + cos(8,) sin(82) %3D
tation by an angle 0 can be written in matrix form as: [cos(0) - sin(0)] sin(0) cos(0) Use this and composition of linear transformations to show the following trigonometric io cos(0, + 02) = cos(01) cos(02) – sin(61) sin(02) sin(61 + 02) = sin(81) cos(02) + cos(8,) sin(82) %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![8. In the lectures, we saw that the linear transformation of counter-clockwise rotation about the origin
by an angle 0 can be written in matrix form as:
[cos(0) - sin(0)]
[ sin(e) cos(e)
cos(0)
Use this and composition of linear transformations to show the following trigonometric identities:
cos(01 + 02) = cos(04) cos(02) – sin(@1) sin(@2)
%3D
sin(0, + 02) = sin(01) cos(02) + cos(61) sin(@2)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1aaff698-d6d9-432c-a8ab-5a03f6066bc1%2F9f77a07b-5abd-425c-a4cf-e1b230357369%2Fyswqmhg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8. In the lectures, we saw that the linear transformation of counter-clockwise rotation about the origin
by an angle 0 can be written in matrix form as:
[cos(0) - sin(0)]
[ sin(e) cos(e)
cos(0)
Use this and composition of linear transformations to show the following trigonometric identities:
cos(01 + 02) = cos(04) cos(02) – sin(@1) sin(@2)
%3D
sin(0, + 02) = sin(01) cos(02) + cos(61) sin(@2)
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