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Find the transformation matrix that rotates a rectangular coordinate system through an angle of 60 about axes equal angels with original three coordinate axes

User Ollifant
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1 Answer

14 votes
14 votes

Answer:


M = \left[\begin{array}{ccc}cos \ 60&0\\0&-sin \ 60\end{array}\right]

Step-by-step explanation:

To find the matrix, let's decompose the vectors, the rotated angle is (-60C) for the prime system

x ’= x cos (-60)

y ’= y sin (-60)

we use

cos 60 = cos (-60)

sin 60 = - sin (-60)

we substitute

x ’= x cos 60

y ’= - y sin 60

the transformation system is


\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}cos 60&0\\0&-sin60\end{array}\right] \ \left[\begin{array}{ccc}x\\y\end{array}\right]x '

the transformation matrix is


M = \left[\begin{array}{ccc}cos \ 60&0\\0&-sin \ 60\end{array}\right]

User Peterw
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