Hyperbolic functions

Worked examples (6)

• 1Evaluating sinh and cosh from the definition
• 2Writing tanh in exponential form
• 3Proving cosh²x − sinh²x = 1
• 4Proving the double-angle identity for sinh
• 5Solving a hyperbolic equation via a quadratic in eˣ
• 6Solving an equation using cosh² − sinh² = 1

Model answers (6)

• ✓Model answer 1
• ✓Model answer 2
• ✓Model answer 3
• ✓Model answer 4
• ✓Model answer 5
• ✓Model answer 6

Worked examples (6)

• 1Key features of y = sinh x
• 2Key features of y = cosh x
• 3Asymptotes of y = tanh x
• 4Sketching y = sech x
• 5Sketching y = coth x
• 6Why sinh resembles a flattened cubic

Model answers (6)

• ✓Model answer 1
• ✓Model answer 2
• ✓Model answer 3
• ✓Model answer 4
• ✓Model answer 5
• ✓Model answer 6

Worked examples (6)

• 1Evaluating arsinh using the log form
• 2Evaluating arcosh (positive root only)
• 3Deriving the log form of arsinh
• 4Deriving the log form of artanh
• 5Why arcosh uses the positive root
• 6Solving an equation using an inverse hyperbolic function

Model answers (6)

• ✓Model answer 1
• ✓Model answer 2
• ✓Model answer 3
• ✓Model answer 4
• ✓Model answer 5
• ✓Model answer 6