Trigonometry Calculator
Calculate sin, cos, tan, cosec, sec, and cot for any angle in degrees or radians.
By Syed Mubashir Ali · Last updated
Worked example: how tall is the tree?
You stand 20 metres from a tree and measure the angle to the top as 35°. The height is 20 × tan(35°). Enter 35, check degrees mode, and read tangent: about 0.7002. Multiply by 20 and the tree is roughly 14 metres tall: plus your eye height, which people always forget. Add 1.7 metres and call it 15.7.
Now watch what happens in the wrong mode. In radians, tan(35) is about 0.473, giving 9.5 metres: wrong by a third, and nothing flags it. This is the single most useful habit the calculator can teach: glance at the mode before every trigonometric calculation, the way you glance at the units before every measurement.
The six functions and what they are for
Sine, cosine, and tangent do most of the work: opposite over hypotenuse, adjacent over hypotenuse, opposite over adjacent. SOH-CAH-TOA is the mnemonic, and it survives because it works. The other three are their reciprocals (cosecant is 1/sine, secant is 1/cosine, cotangent is 1/tangent) and they show up where the reciprocal form is the natural one, like sec² in calculus or cosec in wave equations.
For day-to-day triangle problems, learn the big three cold and treat the other three as conveniences. The calculator shows all six together mainly so the reciprocal relationships are visible: if secant is not roughly 1/cosine, you have mistyped something, and that check catches more errors than any amount of careful arithmetic.
How to Use Trigonometry Calculator
- 1Enter an angle and choose whether it is in degrees or radians.
- 2Press Calculate.
- 3You get all six trigonometric functions at once: sine, cosine, tangent and their reciprocals cosecant, secant and cotangent.
- 4The inverse functions are shown alongside, in degrees.
- 5Use the unit circle diagram and the common angle reference table to check the sign and magnitude of your answer.
- 6Compare the decimal answer with the exact-value table: if you see 0.8660, that is √3/2, and most exam answers want the exact form.
Frequently Asked Questions
Why show all six functions rather than one?
Because they are related, and seeing them together makes the relationships visible: cosecant is 1/sine, secant is 1/cosine, cotangent is 1/tangent. It also catches input errors quickly: if the values do not look like reciprocals of each other, you have mistyped something.
What is the difference between degrees and radians?
Two ways of measuring the same angle: a full turn is 360° or 2π radians, so 180° = π radians. Radians are standard in calculus because derivatives of trigonometric functions only take their simple form in radians. Getting the mode wrong is the single most common source of wrong trigonometry answers.
Why is tan(90°) undefined?
Because tangent is sine over cosine, and cos(90°) is zero. Division by zero is undefined, so tangent has a vertical asymptote there and at every 90° plus a multiple of 180°. The same applies to secant, and to cosecant and cotangent at multiples of 180°.
What is the common angle reference table for?
The exact values at 0°, 30°, 45°, 60° and 90° come up constantly and are worth recognising: sin 30° is exactly 1/2, cos 45° is √2/2. A decimal answer of 0.7071 is the same thing, but the exact form is what most exam questions want.
How does the unit circle help?
It shows why the signs change between quadrants. Sine is the vertical coordinate and cosine the horizontal one, so sine is negative below the axis and cosine negative to the left of it. That is far easier to reconstruct than memorising a sign rule.
What is the difference between sin⁻¹ and 1/sin?
Everything. sin⁻¹(x) is the inverse sine: the angle whose sine is x. 1/sin(x) is the cosecant. They look similar written carelessly and mean completely different things: sin⁻¹(0.5) is 30°, while 1/sin(30°) is 2. Mixing them up is one of the most common trigonometry errors, and it survives all the way to university.
Why does my answer disagree with the exact-value table?
Probably the angle mode. The table assumes degrees; if the calculator is in radians, 30 means 30 radians (about 1719°), and every value will be wrong in a way that still looks plausible. Check the mode indicator before anything else. It is the first thing to verify whenever a trigonometry result looks off.
When would I actually need cosecant, secant, or cotangent?
Honestly, less often than sine, cosine, and tangent. They appear in calculus (the derivative of tan is sec²), in physics formulas, and in some engineering contexts. The calculator shows all six because seeing the reciprocal relationships helps you spot input errors, but for most school problems, the big three are enough.
About Trigonometry Calculator
The Trigonometry Calculator evaluates all six trigonometric functions for an angle in degrees or radians, shows the inverse functions, and displays a unit circle and a table of exact values at the common angles. It runs entirely in your browser.
Showing the full set at once is deliberate. The reciprocal relationships (cosecant to sine, secant to cosine, cotangent to tangent) are easier to internalise when you can see the numbers side by side, and an obvious mismatch between them is usually a sign you entered the angle wrong.
The degrees-versus-radians distinction causes more wrong answers than anything else in trigonometry. A full turn is 360° or 2π radians; calculus uses radians because the derivative rules only work cleanly in them. Check the mode before trusting a result.
The unit circle is worth using rather than skipping. Sine is the vertical coordinate and cosine the horizontal one, which makes the sign in each quadrant something you can reason out rather than something to memorise, and it explains why tangent is undefined at 90°, where cosine reaches zero.
A worked example makes the mode issue concrete. Suppose you want sin(30°). In degrees the answer is 0.5: the value every student memorises. Type the same 30 with the calculator in radians and you get −0.988, which is sin(30 radians). Nothing about either answer warns you; both are correct evaluations of different questions. That is why the degrees/radians selector sits right next to the angle box, and why checking it is step zero.