If you need tangent of angle 2θ, cosine of angle 2θ and sine of angle 2θ and you already have angle θ, sin and tan, this calculator does the substitution for you. It suits a quick check, a homework answer you want to confirm, or any figure you need to sanity test.
What Is the Double Angle Formula Calculator?
The double angle formula calculator works through angle θ, sin and tan to give you tangent of angle 2θ, cosine of angle 2θ and sine of angle 2θ.
It is aimed at the case where you know the method but not the arithmetic: schoolwork, a quick check on a worked example, or a figure that needs to be right first time.
How the Double Angle Formula Works
Each step is applied in order and depends only on the values before it, which makes it possible to follow the calculation rather than take it on trust.
If you are working through the same problem by hand afterwards, compare the intermediate values. That is where a mistake usually shows itself.
Checking Your Own Working
Round sensibly as you go and keep the full precision in the calculator. Rounding too early is the most common way of getting a right method to give a wrong answer.
Where a result should be a whole number, such as a count, check it against the constraint that produced it. A fraction of a person is a sign that something upstream needs revisiting.
A Worked Example
Working through an example, with angle θ set to 10, sin set to 5, tan set to 2, the calculator returns sine of angle 2θ of 0.91, and cosine of angle 2θ of 0.41, and tangent of angle 2θ of 2.24. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out tangent of angle 2θ?
Enter angle θ, sin and tan. The calculator then works through the relationship and reports tangent of angle 2θ, cosine of angle 2θ and sine of angle 2θ.
What does the double angle formula actually calculate?
It takes angle θ, sin and tan and converts them into tangent of angle 2θ, cosine of angle 2θ and sine of angle 2θ using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter angle θ?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.
Can I use this for a quick estimate as well as a precise answer?
Yes. The calculator is built for quick checks, so round your inputs to a sensible number of significant figures and the result will be just as useful. If you need more precision, keep the same method and add digits to the inputs rather than adjusting the method itself.