Trigonometry Calculator

Solve the sine, cosine, tangent, cotangent, secant, and cosecant of an angle using the trigonometric functions calculator below.

Solution:

sin(θ): 
cos(θ): 
tan(θ): 
cot(θ): 
sec(θ): 
csc(θ): 


Trigonometry is a branch of mathematics used to solve angles and distances of triangles. While trigonometry covers a lot of ground, the primary concepts revolve around defining and solving the properties of right triangles and the relationships between the distances of the edges and the angles between them.

The major functions of trigonometry are the sine, cosine, tangent, secant, cosecant, and cotangent. These functions define the distances of triangles for a given angle using the unit circle, as shown in the diagram below.

Chart showing the six primary trigonometric functions and the properties they define

How to find sin, cos, tan, cot, sec, & csc

The major functions used in trigonometry are each abbreviated with three-letters. The table below shows the primary trigonometric functions and their abbreviations.

Primary trigonometric functions and their abbreviations.
Function Abbreviation
Sine sin
Cosine cos
Tangent tan
Cosecant csc
Secant sec
Cotangent cot

The first three functions define the relationship between the angles of a triangle and its edges. The table below shows the definitions of each of the three primary functions.

Equations for the three primary trigonometric functions
Sine sin(θ) = oppositehypotenuse
Cosine cos(θ) = adjacenthypotenuse
Tangent tan(θ) = oppositeadjacent

The second three functions are the reciprocal of the primary functions. The table below shows their equations.

Equations for the three reciprocal trigonometric functions
Cosecant csc(θ) = hypotenuseopposite csc(θ) = 1sin(θ)
Secant sec(θ) = hypotenuseadjacent sec(θ) = 1cos(θ)
Cotangent cot(θ) = adjacentopposite cot(θ) = 1tan(θ)

The calculator above will solve all six properties given an angle in degrees or radians.

You might also be interested in our Pythagorean Theorem calculator.