Double Angle Formulas
Trig of 2θ.
Key idea
Trig of 2θ.
In depth
Setting A = B in the sum formulas gives sin 2θ = 2 sin θ cos θ and cos 2θ = cos²θ − sin²θ = 2cos²θ − 1 = 1 − 2sin²θ. tan 2θ = 2tan θ/(1 − tan²θ).
Worked example
If sin θ = 3/5 and cos θ = 4/5, sin 2θ = 24/25, cos 2θ = 7/25.
Formula
Real-world uses
- Simplifying integrals in calculus
- Analysing the motion of a pendulum or a wave pattern
Common mistake
Writing sin 2θ = 2 sin θ.
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 Double Angle Formulas?
Trig of 2θ. It is a topic at the advanced level in Trigonometry.
What is the formula for Double Angle Formulas?
The key formula is sin2θ = 2 sinθ cosθ; cos2θ = cos²θ − sin²θ.
Where is Double Angle Formulas used in real life?
Real-world examples: Simplifying integrals in calculus; Analysing the motion of a pendulum or a wave pattern.
What should I learn before Double Angle Formulas?
Make sure you are comfortable with Sum and Difference Formulas, the previous topic in Trigonometry.
What is a common mistake with Double Angle Formulas?
Writing sin 2θ = 2 sin θ.
How can I practise Double 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 Double Angle Formulas?
Move on to Half Angle Formulas next.
Related advanced topics in Trigonometry
- Graph of Tangent – Periodic with vertical asymptotes at odd multiples of π/2.
- Phase Shift – Horizontal translation of a wave.
- Vertical Shift and Midline – Moves the wave up or down.
- General Sinusoid – Combine amplitude, period, phase and shift.
- Graphs of Reciprocal Trig Functions – Secant, cosecant and cotangent graphs.
- Pythagorean Identity – The key identity from the unit circle.