Exact Value of sin18°
Derivation using pentagon properties.
Key idea
Derivation using pentagon properties.
In depth
Let θ = 18°, so 5θ = 90°. Then sin 2θ = cos 3θ, which leads to 4s² + 2s − 1 = 0 with s = sin 18°, giving sin 18° = (√5 − 1)/4.
Worked example
sin 18° = (2.236 − 1)/4 ≈ 0.309.
Formula
Real-world uses
- Constructing a regular pentagon and understanding the golden ratio in geometry
Common mistake
Picking the negative root of the quadratic.
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 Exact Value of sin18°?
Derivation using pentagon properties. It is a topic at the expert level in Trigonometry.
What is the formula for Exact Value of sin18°?
The key formula is sin18° = (√5−1)/4.
Where is Exact Value of sin18° used in real life?
Real-world examples: Constructing a regular pentagon and understanding the golden ratio in geometry.
What should I learn before Exact Value of sin18°?
Make sure you are comfortable with Product of Trig Values, the previous topic in Trigonometry.
What is a common mistake with Exact Value of sin18°?
Picking the negative root of the quadratic.
How can I practise Exact Value of sin18°?
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 Exact Value of sin18°?
Move on to Haversine Formula 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).