Double Angle Calculator
Find sin 2θ, cos 2θ and tan 2θ for any angle.
Change the values and press Calculate to work out your own figures.
Enter an angle θ and choose degrees or radians.
Show the working
- sin 2θ = 2 sin θ cos θ
- cos 2θ = cos² θ − sin² θ
- tan 2θ = 2 tan θ ÷ (1 − tan² θ)
How to use it
Enter an angle θ and choose degrees or radians.
Enter the values you know (decimals, fractions, surds such as 2√5, or angles such as π/3 in radians). Show the working gives the rule used at each step.
Key facts
sin 2θ = 2 sin θ cos θ; cos 2θ = cos² θ − sin² θ; tan 2θ = 2 tan θ ÷ (1 − tan² θ)
Three forms of cos 2θ
cos 2θ = cos² θ − sin² θ = 2cos² θ − 1 = 1 − 2sin² θ.
Questions
What is sin 2θ for θ = 25°?
sin 50° ≈ 0.7660444431.
And tan 2θ at 45°?
Undefined (tan 90°).
Formulas
sin 2θ = 2 sin θ cos θ; cos 2θ = cos² θ − sin² θ; tan 2θ = 2 tan θ ÷ (1 − tan² θ)
Sources
Limitations
- Angles can be typed in degrees or radians; radians may be written with π (π/3, 2pi/3).