Title Theory.pdf ✅

  Digital Pvt. Ltd. [1] Trigonometry Introduction to Angle Consider a revolving line OP. Suppose that it revolves in anticlockwise direction starting from its initial position OX . The angle is defined as the amount of revolution that the revolving line makes with its initial position. From fig. the angle covered by the revolving line OP is  = POX The angle is taken positive if it is traced by the revolving line in anticlockwise direction. The angle is taken negative if it is covered in clockwise direction. 1° = 60' (minute) 1' = 60" (second) 1 right angle = 90° (degrees) also 1 right angle = 2  rad (radian) One radian is the angle subtended at the centre of a circle by an arc of the circle, whose length is equal to the radius of the circle. 1 rad = 180   57.3° Units of Angle Practical units : degrees (°) 1° = 60'(minute) 1' = 60"(second) To convert an angle from degree to radian multiply it by 180   To convert an angle from radian to degree multiply it by 180  Relation between Angle and Arc Introduction to Angle Part - 01 TG: @Chalnaayaaar
Basic Maths Part-01   Digital Pvt. Ltd. [2] Radian 1 rad = 180° π ≈ 57.3° Illustration 1. Convert the given angles in desired units. (i) 5° to minutes (ii) 6' to seconds (iii) 120" to minutes Solution. (i) 1° = 60' 5° × 60' = 300' (ii) 1' = 60" 6' × 60" = 360" (iii) 60" = 1' 120" 2' 60" = Illustration 2. Convert the given angles in desired units. 1. Convert 45° to radians 2. Convert 5 6  rad to degree Solution. 1. 45 radians 180 4    =  2. 5 180 150 6    =   TG: @Chalnaayaaar
  Digital Pvt. Ltd. [1] Pythagoras Theorem P 2 + B2 = H2 Pythagorean Triplets 3, 4, 5 (32 + 42 = 52 ) 6, 8, 10 (62 + 82 = 102 ) 7, 24, 25 (72 + 242 = 252 ) 12, 16, 20 (122 + 162 = 202 ) Remember for fast calculations in Physics!! Trigonometric Ratios (or T ratios) P sin H = H cosec P = B cos H = H sec B = P tan B = B cot P = It can be easily proved that : 1 cosec sin  =  1 sec cos  =  1 cot tan  =  Pythagoras Theorem and Trigonometric Ratio Part - 02 TG: @Chalnaayaaar
Basic Maths Part-02   Digital Pvt. Ltd. [2] Trigonometric Identities sin2 + cos2 = 1 1 + tan2 = sec2 1 + cot2 = cosec2 Illustration 1. Given sin = 3/5. Find all the other T-ratios, if  lies in the first quadrant. Solution. In OMP, sin = 3 5 so, MP = 3 and OP = 5 OM = 2 2 (5) (3) − = 25 9− = 16 = 4 Now, cos = OM OP = 4 5 tan = MP OM = 3 4 cot = OM MP = 4 3 sec = OP OM = 5 4 cosec = OP MP = 5 3 Table : The T-ratios of a few standard angles ranging from 0° to 90° Angle() 0° 30° 45° 60° 90° sin 0 1 2 1 2 3 2 1 cos 1 3 2 1 2 1 2 0 tan 0 1 3 1 3  (not defined) TG: @Chalnaayaaar