maths class 11 chapter 9 solution

• Our comprehensive Maths Class 11 Chapter 9 Solution will ensure you're fully prepared for your exams.
• Definition of trigonometry and concept of angles.
• What is a Sexagesimal system
• Definition of a circular system
• Definition of Radian with examples
• Solution of each question of Exercise 9.1 in the 1st year Mathematics of the Punjab Textbook Boards.
• Angle in the standard reposition and Trigonometric function
• Solution of each question of Exercise 9.2 in the 1st year Mathematics of the Punjab Textbook Boards.
• Solution of each question of Exercise 9.3 in the 1st year Mathematics of the Punjab Textbook Boards.
• Definition of period: Solution of each question of Exercise 9.4 in the 1st year Mathematics of the Punjab Textbook Boards.
• General Angle (Coterminal Angles): There can be many angles with the same initial and terminal sides. These are called coterminal angles. Consider an angle ∠POQ with initial side OP and terminal side OQ.
• Angle In The Standard Position: An angle is said to be in standard position if its vertex lies at the origin of a rectangular coordinate system and its initial side along the positive x-axis. The following igures show four angles in standard position.
• An angle in standard position is said to lie in a quadrant if its terminal side lies in that quadrant. In the above igure: Angle a lies in I Quadrant as its terminal side lies is I Quadrant Angle b lies in II Quadrant as its terminal side lies is II Quadrant Angle g lies in III Quadrant as its terminal side lies is III Quadrant and Angle q lies in IV Quadrant as its terminal side lies is IV Quadrant If the terminal side of an angle falls on x-axis or y-axis, it is called a quadrantal angle.
• Trigonometric Functions: Consider a right triangle ABC with ∠ = 90 C and sides a, b, c, as shown in the igure. Let m A ∠ =q radian. The side AB opposite to 90° is called the hypotenuse (hyp), The side BC opposite to q is called the opposite (opp) and the side AC related to angle q is called the adjacent (adj).
• In fact these ratios depend only on the size of the angle and not on the triangle formed. Therefore, these ratios are called trigonometric functions of angle q and are deined as below:
• Note: These deinitions are independent of the position of the point P on the terminal side i.e., q is taken as any angle.
• Signs of the Trigonometric functions. If q is not a quadrantal angle, then it will lie in a particular quadrant. Because r xy = + is always positive, it follows that the signs of the trigonometric functions can be found if the quadrant of 0 is known. For example, (i) If q lies in Quadrant I, then a point P(x, y) on its terminal side has both x, y co-ordinates.
• If q lies in Quadrant II, then a point P(x, y) on its terminal side has negative x-coordinate and positive y-coordinate.
• If q lies in Quadrant III, then a point P(x, y) on its terminal side has negative x-coordinate and negative y-coordinate.
• If q lies in Quadrant IV, then a point P(x, y) on its terminal side has positive x-coordinate and negative y-coordinate.
• These results are summarized in the following igure. Trigonometric functions mentioned are positive in these quardrants.