| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Hyperbolic functions |
| Type | Prove hyperbolic identity from exponentials |
| Difficulty | Challenging +1.2 This is a Further Maths question requiring knowledge of hyperbolic functions with complex arguments, but it's a straightforward proof using standard identities (sinh as exponentials or sinh(-x) = -sinh(x) combined with periodicity of exponentials). The 4 marks suggest a routine algebraic manipulation rather than deep insight, making it moderately above average difficulty due to the FM topic but not requiring novel problem-solving. |
| Spec | 4.02n Euler's formula: e^(i*theta) = cos(theta) + i*sin(theta)4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials |
Prove that $\sinh(i\pi - \theta) = \sinh \theta$. [4]
\hfill \mbox{\textit{Edexcel FP3 Q7 [4]}}