# Trigonometry calculator

Make complex trigonometric calculations a breeze with this convenient online tool. Solve a wide range of trigonometric functions including sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Input the angle in degrees or radians, and let the calculator compute the precise values. Get accurate results for both acute and obtuse angles.

## Trigonometric functions calculator

Simplify complex trigonometric calculations with ease using this versatile online tool. Compute the values of sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot) for any given angle in degrees or radians. Simply input the angle and select the desired trigonometric function, and the calculator will provide accurate results.

## Triginometric expression calculator

Simplify and evaluate complex trigonometric expressions effortlessly with this powerful online tool. Whether it's a combination of sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), cotangent (cot), or a mixture of different trigonometric functions, this calculator can handle it all. Input the expression and let the calculator simplify and provide the numerical value.

## What is Trigonometry

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It focuses on the trigonometric functions, which are mathematical functions that relate the ratios of the sides of a right triangle to its angles. The three primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan). These functions are defined based on the ratios of the sides of a right triangle: the sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse, the cosine is the ratio of the adjacent side to the hypotenuse, and the tangent is the ratio of the opposite side to the adjacent side.

Trigonometry has numerous applications in various fields such as physics, engineering, architecture, navigation, and computer graphics. It helps in solving problems related to angles, distances, heights, and velocities using the principles of triangles and trigonometric functions. Trigonometry also provides tools for analyzing periodic phenomena, such as waves and oscillations.

In addition to the primary trigonometric functions, there are reciprocal functions like cosecant (csc), secant (sec), and cotangent (cot), which are defined as the reciprocals of sin, cos, and tan, respectively. Trigonometry also involves identities, formulas, and equations that enable the manipulation and simplification of trigonometric expressions.

## Trigonometric functions

sin *A* = opposite / hypotenuse = *a* / *c*

cos *A* = adjacent / hypotenuse = *b* / *c*

tan *A* = opposite / adjacent = *a* / *b*

csc *A* = hypotenuse / opposite = *c* / *a*

sec *A* = hypotenuse / adjacent = *c* / *b*

cot *A* = adjacent / opposite = *b* / *a*

## Trigonometric Example

Assume we are working with a right-angled triangle where one angle is labeled as θ.

Angle (θ) | Sine (sin(θ)) | Cosine (cos(θ)) | Tangent (tan(θ)) |
---|---|---|---|

0° | 0 | 1 | 0 |

30° | 0.5 | 0.866 | 0.577 |

45° | 0.707 | 0.707 | 1 |

60° | 0.866 | 0.5 | 1.732 |

90° | 1 | 0 | ∞ |

In this example, the table showcases the values of the sine, cosine, and tangent functions for different angles in degrees.

- The sine (sin) function calculates the ratio of the length of the side opposite the angle (θ) to the length of the hypotenuse.
- The cosine (cos) function calculates the ratio of the length of the side adjacent to the angle (θ) to the length of the hypotenuse.
- The tangent (tan) function calculates the ratio of the sine of the angle (θ) to the cosine of the angle (θ).

Please note that the values in the table are rounded for simplicity. Trigonometric functions can be calculated for any angle measure, and you can use the table or a calculator to find the values for different angles.