Product of Trig Values
Special products such as cos36° cos72° = 1/4.
Key idea
Special products such as cos36° cos72° = 1/4.
In depth
Products of cosines at angles in geometric or arithmetic progression often telescope using sin 2x = 2 sin x cos x. For example cos 36° cos 72° = 1/4.
Worked example
cos x cos 2x cos 4x = sin 8x/(8 sin x).
Real-world uses
- Solving olympiad puzzles and evaluating exact sums in higher-level exam questions
Common mistake
Missing the multiplication by sin x at the start.
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 Product of Trig Values?
Special products such as cos36° cos72° = 1/4. It is a topic at the expert level in Trigonometry.
Where is Product of Trig Values used in real life?
Real-world examples: Solving olympiad puzzles and evaluating exact sums in higher-level exam questions.
What should I learn before Product of Trig Values?
Make sure you are comfortable with Range of a Projectile, the previous topic in Trigonometry.
What is a common mistake with Product of Trig Values?
Missing the multiplication by sin x at the start.
How can I practise Product of Trig Values?
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 Product of Trig Values?
Move on to Exact Value of sin18° 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).