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# FP2 Hyperbolics question

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1. There are often questions in paper asking to solve hyperbolic equation.

This is the formula book :

If you look in top example, there are two solutions to cosh(x) = 3, plus and minus. In another paper 2nd picture, there is only one solution to each sinh(x) hyperbolic equation. Why do they sometimes have plus and minus, formula doesn't say plus or minus, so where does that come work?
2. The cosh(x) graph is a many to one graph, so there is two solutions when solving. The sinh(x) graph is a one to one graph and so there is only one solution.
3. It's kinda like an y=x3 graph always having 1 solution for one input while the y=x2 graph always has 2 inputs and one solution. Using these graphs in particular as they have a similar shape to the cosh(x) and sinh(x) graphs
4. (Original post by Bealzibub)
...
Look at the graphs of cosh and sinh. You'll see that cosh lacks injectivity whilst sinh is perfectly injective.

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Updated: June 25, 2016
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