Trigonometry is the branch of geometry that studies the measurement of the sides and angles of triangles. There are six trigonometric functions of note: sine, cosine, tangent, secant, cosecant, and cotangent. Given the measure of an angle in either radians or degrees, this calculator will give you the value of each of those functions for that angle. This is explained more in depth in section 3 below. One major use of trigonometry is to find unknown side lengths and angle measurements of a triangle. For example, if you know the length of two sides of a triangle and the measurement of two angles of that triangle, our calculator can take that information and apply trigonometric rules to find the missing side length and missing angle measurement. For more information, see section 4 of this article.
Hipparchus, a Greek astronomer who lived from ~180 B. C. to ~125 B. C., is thought to be the first individual to write a text on trigonometry. The word trigonometry itself comes from two Greek words, as the Greek root “trigōnon” means triangle and the Greek root “metron” means measure. However, many significant advances in the history of trigonometry were actually first achieved by Indian mathematicians. For example, the first table of sine values that was accurate to four decimal places was completed by the Indian mathematician Aryabhata in the 5th century A.D. Nowadays, trigonometry is highly relevant for many real-world applications, including modern astronomy and GPS navigation. Trigonometry is also used throughout modern physics to model light waves, sound waves, and many other phenomena. It is tough to understand many aspects of modern technology without understanding trigonometry!
Each of the six trigonometric functions listed above—sine (sin), cosine (cos), tangent (tan), secant (sec), cosecant (csc), and cotangent (cot)—takes an angle as input and gives a real number as output. The sine of an acute angle α of a right triangle will equal the fraction calculated by dividing the length of the side across from that angle by the length of the hypotenuse of that triangle. Our calculator will automatically give you the value of all six functions for the angle you enter. You can enter the angle in either degrees or radians, so feel free to use whichever units you prefer.
To find the missing sides or angles of a right triangle, all you need to do is enter the known measurements into this trigonometry calculator. This calculator will be able to find the missing side lengths and angles if you enter (1)two side lengths, (2)one side length and one acute angle, or (3)one side length and the area of the triangle. It is important to notice that just knowing all three angles of the triangle is not enough information to find any of the side lengths. This is because two triangles can have exactly the same angle measurements but different side measurements; two triangles with identical angle measurements are called similar triangles. For two triangles to have identical angles and identical side lengths, they have to be congruent triangles.