How to use this trigonometry calculator
This trigonometry calculator will help you in two popular cases when trigonometry is needed. If you want to find the values of sine, cosine, tangent, and their reciprocal functions, use the first part of the calculator. Are you searching for the missing side or angle in a right triangle using trigonometry? Our tool is also a safe bet! Type 2–3 given values in the second part of the calculator, and you'll find the answer in a blink of an eye.
There are many other useful tools when dealing with trigonometry problems. Check out two popular trigonometric laws with the law of sines calculator and our law of cosines calculator, which will help you to solve any kind of triangle.
How to use this trigonometry calculator
This trigonometry calculator has two sections that perform two different functions using trigonometry. The following instructions should help you work your way around this calculator with ease:
Part 1 — Trigonometric function values
The first section takes an angle input and gives you a list of trigonometric function values for this angle.
- Select your preferred angle unit: degrees, radians, or gradians.
- Enter the angle value and click Calculate.
- The calculator instantly returns sin, cos, tan, csc, sec, cot.
For example, to find the value of sin(45°), we merely enter 45 degrees as the angle. The calculator instantly tells you that sin(45°) = 0.70710678. It also gives the values of other trig functions, such as cos(45°) and tan(45°).
Part 2 — Right triangle solver
The second section uses trigonometry to determine the missing parameters of a right-angled triangle:
- Select your measurement system: metric (mm, cm, m, km) or US Imperial (in, ft, yd, mi).
- Choose the length unit that suits your problem.
- Start entering the known parameters of the triangle — at least 2 values are required.
- Available inputs: sides a (opposite), b (adjacent), c (hypotenuse); angles α and β; and Area.
- Click Solve Triangle and the calculator will fill in all missing values.
Refer to the diagram shown in the results to understand the labels. For example, if we know two sides, a = 7 m and b = 12 m, we enter them in this calculator. Right away, we see that c = 13.892 m, α = 30.256°, and β = 59.744°.
What is trigonometry?
Trigonometry is a branch of mathematics. The word itself comes from the Greek trigōnon (which means "triangle") and metron ("measure"). As the name suggests, trigonometry deals primarily with angles and triangles; in particular, it defines and uses the relationships and ratios between angles and sides in triangles. The primary application is thus solving triangles, precisely right triangles, and any other type of triangle you like.
The six fundamental trigonometric functions are:
- sin(α) — Sine: ratio of the opposite side to the hypotenuse
- cos(α) — Cosine: ratio of the adjacent side to the hypotenuse
- tan(α) — Tangent: ratio of the opposite side to the adjacent side
- csc(α) — Cosecant: reciprocal of sine (1 / sin α)
- sec(α) — Secant: reciprocal of cosine (1 / cos α)
- cot(α) — Cotangent: reciprocal of tangent (1 / tan α)
Trigonometry as a tool for solving right triangles
A right triangle has one angle equal to 90°. The other two angles, α and β, always add up to 90° as well. Its sides are labelled:
- a — the side opposite to angle α
- b — the side adjacent to angle α (opposite to β)
- c — the hypotenuse (the longest side, opposite the right angle)
The Pythagorean theorem connects the three sides: a² + b² = c².
With trigonometry you can solve for missing sides or angles given any two known measurements. This makes our calculator an ideal companion for geometry, engineering, architecture, navigation, and physics problems.
Measurement systems supported
This calculator supports both the US/Imperial system (inches, feet, yards, miles) and the metric system (millimetres, centimetres, metres, kilometres). Simply choose the system that applies to your problem before entering values.
Meet the creator of our trigonometry calculator
This calculator was built by the CalcuGo team to provide a fast, accurate, and multilingual trigonometry tool accessible to students, teachers, engineers, and curious minds around the world.
FAQs
How many values do I need to provide to solve a right triangle?
You need at least 2 known values (from sides a, b, c, angles α, β, or the area) to uniquely solve a right triangle. Enter them and the calculator will find the rest.
Can I use radians instead of degrees?
Yes! In Part 1, you can freely switch between degrees, radians, and gradians. The angle in Part 2 (right triangle) is always in degrees.
What is the difference between sin and csc?
Cosecant (csc) is the reciprocal of sine: csc(α) = 1 / sin(α). Similarly, sec = 1 / cos, and cot = 1 / tan.
What if tan or cot is undefined?
Tangent is undefined when cos(α) = 0, i.e., at 90°, 270°, etc. Cotangent is undefined when sin(α) = 0, i.e., at 0°, 180°, etc. The calculator will show ∞ in those cases.
Which measurement units does the right triangle solver support?
Metric: mm, cm, m, km | US Imperial: in (inches), ft (feet), yd (yards), mi (miles). All values are assumed to be in the same unit — the calculator does not convert between them.