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# FP1 matrices help :/ watch

1. Thought I understood matrices until I tried to do the MEI topic assessment:

With q1 part 1, to find the centre of rotation, I used the technique for finding an invariant point and got (0,0) but I have no idea how to find the angle of rotation?
We were told that rotation matrices are of the form:
(cosa, sina)
(-sina, cosa)
which represents a rotation of a degrees, anticlockwise about the origin.

But doing the inverse cos and inverse sin gives me 106 and 74 degrees, so how can it be two angles?
2. (Original post by surina16)
Thought I understood matrices until I tried to do the MEI topic assessment:

With q1 part 1, to find the centre of rotation, I used the technique for finding an invariant point and got (0,0) but I have no idea how to find the angle of rotation?
We were told that rotation matrices are of the form:
(cosa
So, if you use the formula provided in your formula book, you know the values of cos a and sin a, consequently you can find a. Note that .
3. (Original post by surina16)
Thought I understood matrices until I tried to do the MEI topic assessment:

With q1 part 1, to find the centre of rotation, I used the technique for finding an invariant point and got (0,0) but I have no idea how to find the angle of rotation?
We were told that rotation matrices are of the form:
(cosa, sina)
(-sina, cosa)
which represents a rotation of a degrees, anticlockwise about the origin.

But doing the inverse cos and inverse sin gives me 106 and 74 degrees, so how can it be two angles?
You could also look at the base vectors and see where they are transformed to - I prefer this to remembering stuff. Easy to get the angle from that ...
4. (Original post by Mr M)
So, if you use the formula provided in your formula book, you know the values of cos a and sin a, consequently you can find a. Note that .
Thank you so much! Completely forgot that sin74 = sin106 etc
5. (Original post by surina16)
...
Note that the very first part says "state the centre of rotation". No working out is expected or required. This centre is always the origin for a rotation matrix with standard cartesian coordinates.

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