Because of the “2x” in 2x - 2, there will be 2 cycles worth of answers, and as a result, there will be twice the number of solutions as before (applies mainly to cos and tan, but sin is trickier at times).

As it turns out, 2x - 2 must lie between -2 and 10.566, so that x will lie between 0 and 2pi after transformation.

We pick out angles from the first cycle (0 to 2pi). Then we pick out from the second cycle (2pi to 4pi, found by adding our answers in the first cycle by 2pi).

However, we soon run into trouble as the fourth angle that we have found is rejected. This does not mean that there will only be three solutions. In fact, there remains to be four solutions in total, so we need to extract one “replacement” angle from “the past”.

In other words, we must find one angle from the cycle before the first, found by subtracting our answers in the first cycle by 2pi. One of these new angles will be accepted.

Now that we have our four angles for 2x - 2, we then proceed to find the values of x. Remember to check that the values of x indeed lie between 0 and 2pi.

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