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2nd page   C. W 1. Evaluate sin 30° + cos 30° Ans: (√3 + 1 )/ 2 2. Evaluate tan30° tan60° Ans: 1 3. Evaluate sec^2 60° / tan 45° Ans: 4√2 H. W 1. Evaluate sec 60° + sin 30° + cos^2 60° Ans. 11/4 2. Evaluate cot 60° cot 30° tan 45° Ans: 1 2. Evaluate Sin90° / cos30° Ans: 2/√3

Oral Questions: 1. What are the formula for sin A, cos A and tan A?  2. What are the inverses of sin A, cos A and tan A known as?  3. What is the formula of cosec A, sec A and cot A?  C.W. Questions 1. If sec   θ = 5/4, show that  (sinθ - 2cosθ)/(tanθ - cotθ) = 12/7 Ans : b = 4k, h = 5k Hence p = 3k Hence sin θ = 3/5 cos θ = 4/5 tan θ = 3/4 cot θ = 4/3 LHS = (sin θ -  2cos θ )/(tan θ - cot θ )            = (3/5 - 8/5)/(3/4-4/3)          =( -1)/ (-7/12)           = 12/7 = RHS 2. If tan θ = 1/√7, show that (cosec^2  θ- sec^2  θ) /(cosec^2  θ + sec^2  θ)  = 3/4 3. If cosec θ = 2, show that (cot θ +    sin θ                   -----------   ) = 2                1+cos θ    4. In ∆ABC, right angled at B, AB = 12cm and BC = 5 cm. Find the ...

Class work: Q1.  Fill in the blanks:  In the above figure,  sin A = .......  cos A = .......  tan A = .......  cosec A = .,.....  sec A = ...,....  cot A  = ......,  sin C = ....... cos C = ...... tan C = ...... cosec C = .......  sec C = ........  cot C = ........    Q2.  If sin A = 8 /17, find the other trigonometric ratios of angle A. Ans: Let us draw a triangle ABC in which angle B = 90 deg.  Sin A = p/h = 8/17 Let p = 8k h = 17k, where k is a positive number.                        _______ Hence b = √ h2 - p2                     _____________             = √ 289 k2 - 64 k2                   _______                  = √ 225 k2             ...

Quotient relation of T ratios: Theorem  For any acute angle A tan A = sin A / cos A Cot A = cos A/ sin A tan A.cot A = 1 Proof: Consider a right angled triangle ∆ABC in which  angle B = 90 deg.  tan A = p/b = p/h                         .......                           b/h                      = sin A/cos A Prove other formulae like that only Square relation; Theorem For  any acute angle A 1. sin^2  A+ cos^2 A = 1 2. 1 + tan^2 A = sec^ 2 A 3. 1 + cot^2 A = cosec^2 A Proof: 1. p^2 / h^2 + b^2 / h^2  = h^2 / h^2 Prove other formulae like that only

What is Trigonometry?   Ans: It is that Branch of mathematics which deals with the measurement of angles and the problems allied with angles.  Which are the six trigonometric ratios?  Ans :  sin, cos, tan, cosec, sec, cot Let angle A be an acute angle of  of a right angled triangle  ∆ABC. Then  Sin A = perpendicular/hypotenuse Cos A = base / hypotenuse Tan A = perpendicular / base Cosec A = hypotenuse/perpendicular Sec A = hypotenuse/base Cot A = base/perpendicular How to remember these formulae?  Remember the sentence : " Some People Have Curly Brown Hair Tightly Pulled Back " Some=People/Have Curly=Brown/Hair Tightly=Pulled/Back sin A= p/h,  cos A= b/h,  tan A= p/b RECIPROCAL OF MAIN FORMULAE COSEC  A=H/P  SEC A=H/B  COT A= B/P  Reciprocal relation cosec A = 1/ sin A sec A = 1/ cos A cot A = 1/ tan A