Trigonometry Formulas


Trigonometry derived from Greek word trigonon means “triangle” and metron means “measure”. Trigonometry is a branch of mathematics that deal with angles, lengths and heights of triangles and relations between different parts of circles and other geometrical figures. Trigonometry is the foundation of all applied geometry, including geodesy, surveying, celestial mechanics, solid mechanics, navigation.

There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

Trigonometry developed from a need to compute angles and distances in such fields as astronomy, mapmaking, surveying, and artillery range finding. Problems involving angles and distances in one plane are covered in plane trigonometry. Applications to similar problems in more than one plane of three-dimensional space are considered in spherical trigonometry.
There is an enormous number of uses of trigonometry and trigonometric functions. For instance, the technique of triangulation is used in astronomy to measure the distance to nearby stars, in geography to measure distances between landmarks, and in satellite navigation systems. The sine and cosine functions are fundamental to the theory of periodic functions, such as those that describe sound and light waves.

Trigonometric table

The Trigonometrical ratios table helps to find the values of trigonometric standard angles such as 0°, 30°, 45°, 60° and 90°. The values of trigonometrical ratios of standard angles are very important to solve the trigonometrical problems. Therefore, it is necessary to remember the value of the trigonometrical ratios of these standard angles. Another important application of trigonometric tables is for Fast Fourier Transform algorithms.

Angles (In Degrees) 0 30 45 60 90 180 270 360
sin 0 12 12–√ 3–√2 1 0 1 0
cos 1 3–√2 12–√ 12 0 1 0 1
tan 0 13–√ 1 3–√ Not Defined 0 Not Defined 1
cot Not Defined 3–√ 1 13–√ 0 Not Defined 0 Not Defined
csc Not Defined 2 2–√ 23–√ 1 Not Defined 1 Not Defined
sec 1 23–√ 2–√ 2 Not Defined 1 Not Defined 1