Pre-Calculus 12 Unit 6 Send-In Assignment On-Line Course SEND - IN ASSIGNMENT UNIT 6 TRIGONOMETRIC EQUATIONS & IDENTITIES Name: _________________________________________ Teacher:________________________________________ School:_________________________________________ Total ______ = _________% 95 Version 1 2012 Page 1 of 16 Unit 6 Pre-Calculus 12 Unit 6 Send-In Assignment On-Line Course All answers rounded to 2 decimal places unless otherwise stated. Show all work where possible. 1. Within the domain 02x , how many solutions are there for the following equations. a) cos5 x 0. 78 a) _____________________________ 1 mark 1 b) sin 3x 2 b) _____________________________ 1 mark c) tan 4x 12 c) _____________________________ 1 mark d) tan bx 5 d) _____________________________ 1 mark 2. For the equation cos 2x 0. 32 a) solve for x , where 02x a) _____________________________ 2 marks b) determine the general solution. b) _____________________________ 2 marks Version 1 2012 Page 2 of 16 Unit 6 Pre-Calculus 12 For the equation 3sinxx 3. Unit 6 Send-In Assignment On-Line Course , solve for x and determine all solutions. 3) _____________________________ 2 marks For the equation cos2 xx 4cos 4. 2 0 a) solve for x , where 0 x 360 a) _____________________________ 2 marks b) determine the general solution. b) _____________________________ 2 marks 5. Solve the following equations algebraically, where 0 x 360 . Give answers as exact solutions. a) 3 tan x 1 a) ____________________________ 2 marks Version 1 2012 Page 3 of 16 Unit 6 Pre-Calculus 12 Unit 6 Send-In Assignment On-Line Course b) sec x 2 b) _____________________________ 2 marks c) cos xx 3 cos c) _____________________________ 2 marks d) 3 tan2 x 1 d) _____________________________ 3 marks Version 1 2012 Page 4 of 16 Unit 6 Pre-Calculus 12 6. Unit 6 Send-In Assignment Solve the following equations algebraically, where 02x Give answers as exact solutions. a) 2sin 2 xxsin On-Line Course . 0 a) _____________________________ 3 marks b) 2cos 2 xx 3cos 1 0 b) _____________________________ 3 marks Version 1 2012 Page 5 of 16 Unit 6 Pre-Calculus 12 c) Unit 6 Send-In Assignment 2 cos2 xxcos On-Line Course 0 c) _____________________________ 3 marks d) sin 2x 1 2 d) _____________________________ 3 marks Version 1 2012 Page 6 of 16 Unit 6 Pre-Calculus 12 Unit 6 Send-In Assignment On-Line Course 13 e) cos x 22 e) _____________________________ 3 marks 7. Simplify using the sum and difference identities. 3 a) cos x 2 a) _____________________________ 2 marks Version 1 2012 Page 7 of 16 Unit 6 Pre-Calculus 12 Unit 6 Send-In Assignment b) If tan xxis 1, simplify tan 3 On-Line Course . Answer exact value and rationalize denominator. b) _____________________________ 3 marks c) sin xx cos 36 c) ___________________________ 3 marks Version 1 2012 Page 8 of 16 Unit 6 Pre-Calculus 12 Unit 6 Send-In Assignment On-Line Course d) cos3xcos5 x sin 3xsin 5x d) _____________________________ 2 marks e) sin 6. 7cos 2. 3 cos 6. 7sin 2. 3 e) _____________________________ 2 marks 17 f) Find the exact value of sin Hint: use sum identity 12 f) _____________________________ 3 marks Version 1 2012 Page 9 of 16 Unit 6 Pre-Calculus 12 Unit 6 Send-In Assignment g) Find the exact value of cos AB tan A On-Line Course given: 2 2 if angle A is in quadrant 1 and cos B if angle B is in quadrant 3. 5 3 g) _____________________________ 3 marks 8. Write the following as a single trigonometric function. a) cos 24sin 24 a) _____________________________ b) 1 2sin 2 2 marks 6 b) _____________________________ 2 marks Version 1 2012 Page 10 of 16 Unit 6 Pre-Calculus 12 c) Unit 6 Send-In Assignment On-Line Course 1 sin12 cos12 2 c) _____________________________ 2 marks d) 2 tan 4 5 5 tan2 4 d) _____________________________ 2 marks 9. If cos 1 and is in Quadrant III. Evaluate sin 2 . 3 9. _____________________________ 3 marks Version 1 2012 Page 11 of 16 Unit 6 Pre-Calculus 12 10. Determine all restrictions for Unit 6 Send-In Assignment On-Line Course csc . 1 cos 10. _____________________________ 2 marks 11. Prove the following identities. a) cot sec sin 1 3 marks b) cot tan csc sec 3 marks Version 1 2012 Page 12 of 16 Unit 6 Pre-Calculus 12 c) Unit 6 Send-In Assignment sin tan cos 1 On-Line Course tan 3 marks d) cos2 cot 2 1 cot 2 3 marks Version 1 2012 Page 13 of 16 Unit 6 Pre-Calculus 12 e) Unit 6 Send-In Assignment 1 tan 1 cot On-Line Course 1 tan cot 1 3 marks f) tan cos sec csc 3 marks Version 1 2012 Page 14 of 16 Unit 6 Pre-Calculus 12 g) Unit 6 Send-In Assignment sin 1 cos On-Line Course 1 cos sin 3 marks h) sin 2 1 cos 2 cot 3 marks Version 1 2012 Page 15 of 16 Unit 6 Pre-Calculus 12 Unit 6 Send-In Assignment On-Line Course A SUMMARY OF BASIC IDENTITIES AND FORMULAE Pythagorean Identities: sin22 cos 1 tan22 sec 1 1 cot22 csc Reciprocal and Quotient Identities: 1 1 sec csc cos sin tan sin cos cot cot 1 tan cos sin Addition Identities: cos cos cos sin sin cos sin sin cos cos sin sin tan tan 1 tan tan tan tan sin cos cos sin sin cos cos sin tan tan 1 tan tan Double Angle Identities: cos 2 cos22 2 cos 1 Version 1 2012 sin 2 2sin cos sin 2 1 2 2 sin tan 2 Page 16 of 16 2 tan 1 tan 2 Unit 6