1st Year Math Notes Chapter 9
Important Short Notes of 1st Year Math Notes Chapter 9 written by Professor Asad Khalid Suib. These notes are very helpful in the preparation of Fundamentals of Trigonometry for the students of Mathematics of the Intermediate and these are according to the paper patterns of all Punjab boards.
Summary and Contents:
Topics which are discussed in the notes are given below:
- Our comprehensive 1st Year Math Notes Chapter 9 will ensure you're fully prepared for your exams.
- Important Short and Long Questions of Chapter No. 9: Fundamentals of Trigonometry in Mathematics Class 11.
- Definition of quadrantal angle with example
- Definition of Conterminal angles with example
- Definition of General angle with example
- Trigonometry is an important branch of Mathematics. The word Trigonometry has been derived from three Greek words: Trei (three), Goni (angles) and Metron (measurement). Literally it means measurement of triangle. For study of calculus it is essential to have a sound knowledge of trigonometry. It is extensively used in Business, Engineering, Surveying, Navigation, Astronomy, Physical and Social Sciences.
- Units of Measures of Angles: Concept of an Angle Two rays with a common starting point form an angle. One of the rays of angle is called initial side and the other as terminal side. The angle is identiied by showing the direction of rotation from the initial side to the terminal side. An angle is said to be positive/negative if the rotation is anti-clockwise/clockwise. Angles are usually denoted by Greek letters such as a (alpha), b (beta), g (gamma), q (theta) etc.In igure 9.1 ∠AOB is positive and ∠COD is negative.
- Sexagesimal System: (Degree, Minute and Second). If the initial ray OA rotates in anti-clockwise direction in such a way that it coincides with itself, the angle then formed is said to be of 360 degrees (360°). One rotation (anti-clockwise) = 360°
- 1 / 2 rotation (anti-clockwise) = 180° is called a straight angle
- 1 / 4 rotation (anti-clockwise) = 90° is called a right angle.
- 1 degree (1°) is divided into 60 minutes (60′) and 1 minute ( 1’) is divided into 60 seconds
- (60′′). As this system of measurement of angle owes its origin to the English and because 90,
- 60 are multiples of 6 and 10, so it is known as English system or Sexagesimal system.
- Thus 1 rotation (anti-clockwise) = 360°. One degree (1°) = 60’ One minute (1′) = 60”
- Note: If the value of pi is not given, we shall take pi ≈ 3.1416.
- An arc subtends an angle of 70° at the center of a circle and its length is 132 m.m. Find the radius of the circle.
- Find the length of the equatorial arc subtending an angle of 1° at the centre of the earth, taking the radius of the earth as 6400 km.
- Deinition: Radian is the measure of the angle subtended at the center of the circle by an arc, whose length is equal to the radius of the circle. Consider a circle of radius r. Construct an angle ∠AOB at the centre of the circle whose rays cut of an arc AB on the circle whose length is equal to the radius r. Thus m AOB ∠ = 1 radian.
- Conversion of Radian into Degree and Vice Versa We know that circumference of a circle of radius r is 2 ( ), pr l = and angle formed by one complete revolution is q radian, therefore, l r q. Find correct to the nearest centimeter, the distance at which a coin of diameter ‘1’ cm should be held so as to conceal the full moon whose diameter subtends an angle of 31’ at the eye of the observer on the earth. Let O be the eye of the observer. ABCD be the moon and PQSR be the coin, so that APO and CSO are straight line segments.