Half Angle Formulas
Trig of θ/2.
Key idea
Trig of θ/2.
In depth
Rearranging the double angle formulas: sin(θ/2) = ±√((1 − cos θ)/2), cos(θ/2) = ±√((1 + cos θ)/2). The sign depends on the quadrant of θ/2.
Worked example
cos 15° = √((1 + cos 30°)/2) = √((2 + √3)/4) = (√6 + √2)/4.
Formula
Real-world uses
- Finding exact values from known angles in exam questions and in calculus integration
Common mistake
Choosing the sign without checking the quadrant.
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 Half Angle Formulas?
Trig of θ/2. It is a topic at the expert level in Trigonometry.
What is the formula for Half Angle Formulas?
The key formula is sin²(θ/2) = (1−cosθ)/2.
Where is Half Angle Formulas used in real life?
Real-world examples: Finding exact values from known angles in exam questions and in calculus integration.
What should I learn before Half Angle Formulas?
Make sure you are comfortable with Double Angle Formulas, the previous topic in Trigonometry.
What is a common mistake with Half Angle Formulas?
Choosing the sign without checking the quadrant.
How can I practise Half Angle 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 Half Angle Formulas?
Move on to Power Reducing Formulas next.
Related expert topics in Trigonometry
- 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).
- Trig Equations with Identities – Use identities to factor trig equations.