Finding the angle and direction of rotation from a 2D rotation matrix

5

I've tried to find information about this on the web, but I lack the knowledge to understand most of those explanations at the moment. Some of the explanations I've found
are aimed at a higher level than A-Level and I can't follow them. I know I can use my calculator to draw the graphs and read off the angle where they correspond. Can somebody shine some light on this for me please and suggest another method ?

Reply 1

mqb2766

21

Original post

by Skybird

I've tried to find information about this on the web, but I lack the knowledge to understand most of those explanations at the moment. Some of the explanations I've found
are aimed at a higher level than A-Level and I can't follow them. I know I can use my calculator to draw the graphs and read off the angle where they correspond. Can somebody shine some light on this for me please and suggest another method ?

Your 2*2 matrix is just sin and cos of the same angle, so use any single element to narrow it down to two values of theta, so solve
cos(theta) = R11
say, then use the sign of sin(theta), R21, to choose which of the two values is correct, so which of the two quadrants theta actually lies in.

(edited 11 months ago)

Reply 2

tonyiptony

11

If you know your matrix is indeed a rotation matrix, then you can read off of the first column to see where the vector (1,0) gets map to. Drawing a picture helps.

Reply 3

Finnns

1

A good way to tackle trig equations is by using common unit circle values and inverse functions to get the main solution. From there, account for the function's cycle, 360 degrees (2π) for sine/cosine, 180 degrees (π) for tangent.

Finding the angle and direction of rotation from a 2D rotation matrix

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