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 0 x 2 , how many solutions are there for the following equations. a) cos 5 x 0.78 a) _____________________________ 1 mark 1 b) sin 3 x 2 b) _____________________________ 1 mark c) tan 4 x 12 c) _____________________________ 1 mark d) tan bx 5 d) _____________________________ 1 mark 2. For the equation cos 2 x 0.32 a) solve for x , where cos cos cos sin sin a) _____________________________ 2 marks b) determine the general solution. b) _____________________________ 2 marks Version 1 2012 Page 2 of 16 Unit 6 Pre-Calculus 12 Unit 6 Send-In Assignment On-Line Course For the equation 3sin x x , solve for x and determine all solutions. 3. 3) _____________________________ 2 marks For the equation cos 2 x 4 cos x 2 0 4. 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 x 3 cos x c) _____________________________ 2 marks d) 3 tan 2 x 1 d) _____________________________ 3 marks Version 1 2012 Page 4 of 16 Unit 6 Pre-Calculus 12 6. Unit 6 Send-In Assignment On-Line Course Solve the following equations algebraically, where 0 x 2 . Give answers as exact solutions. a) 2sin 2 x sin x 0 a) _____________________________ 3 marks b) 2 cos 2 x 3cos x 1 0 b) _____________________________ 3 marks Version 1 2012 Page 5 of 16 Unit 6 Pre-Calculus 12 c) Unit 6 Send-In Assignment On-Line Course 2 cos 2 x cos x 0 c) _____________________________ 3 marks d) sin 2 x 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 1 3 e) cos x 2 2 e) _____________________________ 3 marks 7. Simplify using the sum and difference identities. 3 x a) cos 2 a) _____________________________ 2 marks Version 1 2012 Page 7 of 16 Unit 6 Pre-Calculus 12 Unit 6 Send-In Assignment On-Line Course b) If tan x is 1, simplify tan x . Answer exact value and rationalize denominator. 3 b) _____________________________ 3 marks c) sin x cos x 3 6 c) ___________________________ 3 marks Version 1 2012 Page 8 of 16 Unit 6 Pre-Calculus 12 Unit 6 Send-In Assignment On-Line Course d) cos 3 x cos 5 x sin 3 x sin 5 x d) _____________________________ 2 marks e) sin 6.7 cos 2.3 cos 6.7 sin 2.3 e) _____________________________ 2 marks 17 f) Find the exact value of sin 12 Hint: use sum identity f) _____________________________ 3 marks Version 1 2012 Page 9 of 16 Unit 6 Pre-Calculus 12 Unit 6 Send-In Assignment On-Line Course g) Find the exact value of cos A B given: tan A 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) _____________________________ 2 b) 1 2sin 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 tan 2 4 d) _____________________________ 2 marks 9. If cos 1 and is in Quadrant III. Evaluate sin 2 . 3 9. _____________________________ 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 3 marks csc . 1 cos 10. _____________________________ 2 marks 11. Prove the following identities. a) cot sec sin 1 3 marks b) Version 1 2012 cot tan Page 12 of 16 csc sec Unit 6 Pre-Calculus 12 Unit 6 Send-In Assignment On-Line Course 3 marks c) sin tan cos 1 tan 3 marks d) cos 2 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) cos cos cos sin sin 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: sin 2 cos 2 1 1 tan 2 sec2 1 cot 2 csc 2 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 cos cos sin sin tan tan 1 tan tan tan sin sin cos cos sin sin sin cos cos sin tan tan tan 1 tan tan Double Angle Identities: sin 2 2sin cos cos 2 cos 2 sin 2 2 2 cos 1 1 2sin 2 Version 1 2012 Page 16 of 16 Unit 6