trigonometry.md

Index

• Trigonometric functions
  • Sin Theta
  • Cos or Cosin Theta
  • Tan Theta
  • Cosec Theta
  • Sec Theta
  • Cot Theta
• Pythagorus Theorem
• Eucledian Distance
• References

Trigonometry

Trigonometric functions

• The functions sine, cosine and tangent of an angle are sometimes referred to as the primary or basic trigonometric functions. Their usual abbreviations are respectively. Where theta denotes the angle.

Sin Theta

• The sine of an angle is defined, in the context of a right triangle, as the ratio of the length of the side that is opposite to the angle divided by the length of the longest side of the triangle (the hypotenuse).

  

Cos or Cosin Theta

• The cosine of an angle in this context is the ratio of the length of the side that is adjacent to the angle divided by the length of the hypotenuse.

  

Tan Theta

• The tangent of an angle in this context is the ratio of the length of the side that is opposite to the angle divided by the length of the side that is adjacent to the angle. This is the same as the ratio of the sine to the cosine of this angle, as can be seen by substituting the definitions of sin and cos from above:

  

• The remaining trigonometric functions secant (sec ), cosecant (csc ), and cotangent (cot ) are defined as the reciprocal functions of cosine, sine, and tangent, respectively.

• Rarely, these are called the secondary trigonometric functions:

  

Cosec Theta

• cosecant

  

Sec Theta

• secant

  

Cot Theta

• cotangent

  

Pythagorus Theorem

• It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
• This theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation.

  

Eucledian Distance

* The distance between two objects that are not points is usually defined to be the smallest distance among pairs of points from the two objects. * Formulas are known for computing distances between different types of objects, such as the distance from a point to a line. * In advanced mathematics, the concept of distance has been generalized to abstract metric spaces, and other distances than Euclidean have been studied.

Two dimensions

In the Euclidean plane, let point p have Cartesian coordinates (P1, P2) and let point q have coordinates (q1,q2). Then the distance between p and q is given by:

References

• https://towardsdatascience.com/9-distance-measures-in-data-science-918109d069fa