Ada Programming/Mathematical calculations/Trigonometry

From Wikibooks, open books for an open world
Jump to: navigation, search

Trigonometry in Algebra is the study of triangles and how their measurements of different side and angles relate to each other.

Trigonometry is most well known for it's trigonometric functions, namely sin (sine), cos (cosine), and tan (tangent). They are used in relation to angles to discover the measurements of sides in right triangles.

Sin(x) = Opposite Side/Hypotenuse

Cos(x) = Adjacent Side/Hypotenuse

Tan(x) = Opposite Side/Adjacent Side or sin(x)/cos(x)

Note: In trigonometric functions, x represents the measure of an angle (in degrees or radians) in relation to the sides of the right triangle in question.


Other trigonometric functions include csc (cosecant), sec (secant), and cot (cotangent). They are as follows:

Csc(x) = 1/sin(x)

Sec(x) = 1/cos(x)

Cot(x) = 1/tan(x) or cos(x)/sin(x)

While these functions exist to determine the missing length of a side, they assume that the measure of the reference angle is known. If the measure of the sides of a triangle is known, then it is possible to discover the measure of a reference angle with the use of inverse trigonometric functions. They are as follows:

sin^{-1}(Opposite Side/Hypotenuse) = x

cos^{-1}(Adjacent Side/Hypotenuse) = x

tan^{-1}(Opposite Side/Adjacent Side) = x

Note: x is the measure of the reference angle in degrees or radians.