Sine, cosine & tangent calculator
Enter an angle and get sin, cos and tan with the reference triangle shown.
How to use this calculator
Enter any angle, in degrees or radians, and the calculator returns all three primary trig ratios, plus the reference angle it used.
How it works
Degrees are converted to radians internally (radians = degrees × π ÷ 180). Each ratio is computed from the angle’s position on the unit circle, and undefined values (like tan 90°) are reported honestly instead of showing a misleading huge number.
cos θ = adjacent ÷ hypotenuse
tan θ = sin θ ÷ cos θ
Worked example
sin 30°: 30° sits in the first quadrant. sin 30° = 0.5, cos 30° ≈ 0.866, tan 30° ≈ 0.577.
Common mistakes
- Forgetting to switch between degrees and radians, the most common trig error.
- Typing tan 90° and trusting the giant number; it is undefined.
When to use it
Right-triangle problems, physics components, waves, and anywhere angles meet lengths.
Frequently asked questions
A memory aid: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
Because cos 90° = 0, and tan = sin ÷ cos would mean dividing by zero.
Going deeper: reciprocal ratios and a key identity
Each primary ratio has a reciprocal partner. Cosecant is 1 divided by sine, secant is 1 divided by cosine, and cotangent is 1 divided by tangent. They add no new information, but they shorten many formulas, and they explain more undefined cases: wherever sine is zero, cosecant is undefined, just as tangent is undefined wherever cosine is zero.
Signs matter once an angle leaves the first quadrant. Sine is positive in quadrants I and II, cosine is positive in quadrants I and IV, and tangent is positive in quadrants I and III. The identity above is a useful check on any answer: square the sine and cosine you found and confirm the pair adds to 1.
Example: All three ratios at 45 degrees
Step 1, Picture the triangle: At 45 degrees the right triangle is isosceles, so take both legs as 1. The hypotenuse is then sqrt(1^2 + 1^2) = sqrt(2).
Step 2, Apply the ratios: sin(45 degrees) = 1 / sqrt(2), which is about 0.707. Cosine uses the other leg, so cos(45 degrees) is also about 0.707.
Step 3, Tangent and check: tan(45 degrees) = 1 / 1 = 1. The identity check gives 0.707^2 + 0.707^2 = 0.5 + 0.5 = 1, as expected.
Putting the ratios to work
The most common real task is turning a known angle and one known side into a missing side. Rearrange the ratio before you calculate: opposite = hypotenuse * sin(theta), adjacent = hypotenuse * cos(theta), and hypotenuse = opposite / sin(theta). Choosing the ratio that contains both the side you know and the side you want keeps the problem to a single step. The same rearrangement, used in reverse with the inverse functions, turns two known sides into the angle between them. Work through the 45 degree example above by hand once, and the pattern behind every other special angle becomes much easier to trust.
More questions
Cosecant (csc) is 1/sin, secant (sec) is 1/cos, and cotangent (cot) is 1/tan. For example, cos(60 degrees) = 0.5, so sec(60 degrees) = 1 / 0.5 = 2. A reciprocal is undefined wherever its base ratio is zero.
Adding 360 degrees brings a point on the unit circle back to the same position, and sine and cosine are its coordinates, so their values repeat. Tangent repeats sooner, every 180 degrees, because opposite points on the circle give the same ratio of coordinates.