Definitions: FSc Part1 KPK

A Textbook of Mathematics for Class XI is published by Khybar Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan. The book has total of twelve (12) chapters.

Definition of the book provide the quick overview of the book.

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  • Trigonometry: The word trigonometry has been derived from three Greek words Trei (three) Goni (angles) and Metron (measurement). its mean measurement of triangle.
  • Angle: Two rays with common starting point from an angle is called an angle.
  • Degree: If the circumference of circle is divided into $360^\circ$ equal parts in length, the angle subtended by one part at the center of the circle is called a degree.
  • Allied angles: The angles associated with basic angles of measure $\theta$ to the right angle or its multiple are called allied angles. The angles of measure $90^{\circ} \pm \theta, 180^{\circ} \pm \theta, 270^{\circ} \pm \theta, 360^{\circ} \pm \theta$ are known as allied angles.
  • Period: period is the smallest positive number which, when added to the original circular measure of the angle, gives the same value of the function.
  • Circular system (Radians): A radian is the measure of the central angle of an arc of a circle whose length is equal to the radius of the circle.
  • Sexagesimal system: The system of measurement in which the angle is measured in degree, and its sub-units, minutes and seconds is called the Sexagesimal system.
    e.g. $16^\circ 13' 9''$
  • Period of Trigonometric Function: The smallest +ve number which when added to the original circular measurement of the angle gives same value of function is called period.
    e.g. $sin(\alpha+2\pi)=sin\alpha$
  • Trigonometry equation: The equation, containing at least one trigonometry function are called Trigonometry equation.
    e.g. $sin x=\frac{2}{7}$, $cos x-tan x=0$.
  • Oblique Triangles: A triangle, which is not right, is called an oblique triangle.
  • Circum-Circle: The circle passes through the three vertices of a triangle is called circum-circle.
  • In-Circle: A circle drawn inside a triangle touching its three sides is called its inscribed circle or in-circle.
  • Escribed Circles: A circle, which touches one side of the triangle externally and the other two produced sides, is called an escribed circle or ex-circle or e-circle.
  • Trigonometric function: The equation, containing at least one trigonometric function, are called trigonometric function.