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**cozza** (iii) Let rθ be the rotation that completes the required transformation, where θ lies in the interval (−π,π]. Find the exact values of tan θ,cos θand sin θ, and hence write down a formal definition of rθ using two-line notation. (There is no need to work out the value of the angle θ.)

(iv) Find the coordinates of the images of A' and C' under the rotation rθ. Give your answers as exact values.

I have done (i) and (ii) see below, but am unsure about how to work out the rotation without knowing what angle it rotates by. Thanks for your pointers.

(i) $\displaystyle t_{a,b}:R^2 \rightarrow R^2$

$\displaystyle (x,y) \mapsto (x+2,y-1)$

(ii) A' (5,-2) and C' (4,2)

(iii) ?