FP3.1 - Hyperbolic functions

Definition of the six hyperbolic For example, cosh x = 1 (ex + e−x), functions in terms of exponentials.; Graphs and properties of the 1 2 sech x = =. hyperbolic functions. cosh x ex + e−x Students should be able to derive and use simple identities such as cosh2 x − sinh2 x ≡ 1 and cosh2 x + sinh2 x ≡ cosh 2x and to solve equations such as a cosh x + b sinh x = c.

Use fp3.1.1 - definition of the six hyperbolic to connect the rule to the data and decision in the question.

This matters because fp3.1.1 - definition of the six hyperbolic determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.1.1 - definition of the six hyperbolic to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP3.1.1 - Definition of the six hyperbolic is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Understand inverse hyperbolic functions, their graphs, properties and logarithmic forms, including arsinh x = ln(x + √(1 + x²)).

Use fp3.1.2 - inverse hyperbolic functions to connect the rule to the data and decision in the question.

This matters because fp3.1.2 - inverse hyperbolic functions determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.1.2 - inverse hyperbolic functions to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP3.1.2 - Inverse hyperbolic functions is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.