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.

${\displaystyle Sin(x)=OppositeSide/Hypotenuse}$

${\displaystyle Cos(x)=AdjacentSide/Hypotenuse}$

${\displaystyle Tan(x)=OppositeSide/AdjacentSide}$ or ${\displaystyle sin(x)/cos(x)}$

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:

${\displaystyle Csc(x)=1/sin(x)}$

${\displaystyle Sec(x)=1/cos(x)}$

${\displaystyle Cot(x)=1/tan(x)}$ or ${\displaystyle cos(x)/sin(x)}$

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:

${\displaystyle sin^{-1}(OppositeSide/Hypotenuse)=x}$

${\displaystyle cos^{-1}(AdjacentSide/Hypotenuse)=x}$

${\displaystyle tan^{-1}(OppositeSide/AdjacentSide)=x}$

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