Mollweide and Napier Formulas
Alternative triangle-solving identities.
Key idea
Alternative triangle-solving identities.
In depth
Mollweide: (a − b)/c = sin((A − B)/2)/cos(C/2). Each relation involves all six parts of a triangle and is a good check of numerical work for a solved triangle.
Worked example
If a solved triangle fails the check, one of the computed values has an error.
Real-world uses
- Checking triangle solutions in land surveying and in historical navigation methods
Common mistake
Using them as a primary method when the law of sines is simpler.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Mollweide and Napier Formulas?
Alternative triangle-solving identities. It is a topic at the expert level in Trigonometry.
Where is Mollweide and Napier Formulas used in real life?
Real-world examples: Checking triangle solutions in land surveying and in historical navigation methods.
What should I learn before Mollweide and Napier Formulas?
Make sure you are comfortable with Law of Tangents, the previous topic in Trigonometry.
What is a common mistake with Mollweide and Napier Formulas?
Using them as a primary method when the law of sines is simpler.
How can I practise Mollweide and Napier Formulas?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Mollweide and Napier Formulas?
Move on to Heron from Trigonometry next.
Related expert topics in Trigonometry
- Half Angle Formulas – Trig of θ/2.
- Power Reducing Formulas – Reduce squares to first powers of cos 2θ.
- Product-to-Sum Formulas – Convert products into sums.
- Sum-to-Product Formulas – Convert sums into products.
- Triple Angle Formulas – sin3θ and cos3θ in terms of θ.
- Trig and Inverse Trig Compositions – Evaluate expressions like sin(arccos x).