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# C3 Trig Functions Help

1. Hi,

There is a question (no. 7) about an inverse trig function which I really don't understand how to do. I'd be really grateful if someone could explain.

Thanks
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2. Recall that:

By definition, the hypothenuse has a greater length than the adjacent side, so . The ration between and will always be within , but with the unit circle, can be negative, so it will always be within , hence the domain of the function.
Given that is the inverse function of , the domain of is the range of , and the range of the first is the domain of the second.
For ii), you could draw a triangle in a unit circle where such that , and find from there.
For iii), the inverse function is a matter of flipping and and isolating .

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