Hyperbolic functions and their graphsEdexcel A-Level Further Maths: Mind map

Exam questions on Hyperbolic functions and their graphs

1. Let $x=\ln3$.
   Hence, or otherwise, find the value of $\cosh x+\sinh x$.2 marks
2. The functions $f$, $g$ and $h$ are defined for all real $x$ by $f(x)=\sinh x$, $g(x)=\cosh x$ and $h(x)=\tanh x$.
   Explain why the equation $g(x)=\frac12$ has no real solutions.2 marks
3. The equation $\cosh x=\frac{13}{12}$ has two real solutions.
   Use the definition of $\cosh x$ to show that $6e^{2x}-13e^x+6=0$.3 marks