Evaluates the sine, cosine, and tangent of double a given angle, using the standard double-angle trig identities.
How it works
Each double-angle identity combines the sine and cosine of the original angle in its own specific way to give the trig value at twice that angle.
What this does not include
This does not include evaluating the basic sin, cos, and tan of the original angle itself — for that, use this site’s trigonometry calculator instead.
How to use this calculator
- Enter an angle in degrees.
A worked example
At 30°: sin(2×30°) = 0.866, cos(2×30°) = 0.5, tan(2×30°) = 1.7321.
At 45°: sin(90°) = 1, cos(90°) = 0, and tan(90°) is undefined — the same division-by-zero case that shows up in the plain trigonometry calculator.
What the variables mean
| Variable | Meaning |
|---|---|
| Angle | The original angle, in degrees |
| sin2x, cos2x, tan2x | The sine, cosine, and tangent of double that angle |
Edge cases worth knowing
These use the double-angle identities, not a plain lookup at 2× the angle — sin(2x) = 2sin(x)cos(x), for instance — though the numeric result matches evaluating the doubled angle directly.
Doubling an angle to exactly 90° or 270° makes tangent undefined, exactly as it would for any angle landing on those points — the 45° input above is the smallest angle where this happens.
Frequently asked questions
Why is there more than one form of the cos(2x) identity?
Cos(2x) = cos²(x) − sin²(x) is one of several algebraically equivalent forms — it can also be written as 2cos²(x) − 1 or 1 − 2sin²(x), all giving the same result.
When is tan(2x) undefined?
When 2x is 90 degrees (or 90 plus any multiple of 180 degrees), since tangent itself is undefined at those angles.
Where are double-angle formulas commonly used?
Simplifying trig expressions, solving trig equations, and calculus problems involving trigonometric functions frequently rely on these identities.
