- #1

Maybe_Memorie

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## Homework Statement

Prove that the coordinates of the point (x',y') where the counter-clockwise rotation through the angle @ around (0,0) brings the given point (x,y) are

x' = xcos@ - ysin@

y' = xsin@ + ycos@

Hint: show that for the points (x,y) = (1,0) and (x,y) = (0,1) directly,

and use the fact that the vector (x,y) is equal to the combination

x.(1,0) + y.(0,1)

## Homework Equations

For vectors u and v, angle @ between them

u.v = |u||v|Cos@

## The Attempt at a Solution

I don't want to be told how to do it, I would prefer if someone would kind of tease the solution out of me, if you know what i mean..

I've included a diagram, showing my interpretation of the question.

I've tried a few different approaches for the question.

I used the fact that tan@ = (m1 - m2)/(1 +m1m2).

I got the slopes of the lines being y/x and y'/x'. When I plugged everything in and rewrote tan as sin/cos, I got the required formulae, but they were both being divided by each other.

I also used the dot product, put this just resulted with a lot of squares which doesn't help.

I don't entirely understand the hint also.