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TRIGONOMETRY: COMPOUND ANGLE IDENTITIES 07 APRIL 2014 Lesson Description In this lesson, we: Revise the trigonometry from Grade 11 Introduce compound angle identities Introduce double angle identities Summary After some revision on grade 11 work the compound angle identities will be introduced Compound Angle Formulae Double Angle Formulae Test Yourself Question 1 Simplify without the use of a calculator: 2 sin (360 A. o - x) _ -1 cos( x 180 0 ). tan x . sin(90 o x). cos(360 o x) sin(180 o x) B. 1 C. -2 D. 2 E. none of the above Question 2 If 90 0 ; 270 0 , determine 0 cos ( + 80 ) = A. 3 2 without the use of a calculator: sin(300 0 ) cos 45 0 cos 405 0 B. 3 C. 3 2 D. 1 E. none of the above For question 3, 4 and 5 WITHOUT the use of a calculator, determine the value of the following: Question 3 sin 49 0 cos 410 A. 3 2 B. C. 3 1 2 D. 1 E. none of the above D. 1 E. none of the above D. 1 E. none of the above Question 4 0 0 0 0 sin 85 cos 65 + cos 85 sin 65 A. 3 2 B. 1 2 3 C. 3 C. Question 5 1 (cos 15 0 3 sin 15 0 ) 2 A. 2 2 B. 3 2 Question 6 If 13 sin x 5 0 and x [0;270] , determine without the use of a calculator, the value of sin2x. A. 10 26 B. 120 169 C. 120 169 D. 1 E. none of the above D. 1 E. none of the above D. 1 E. none of the above D. p p 2 1 E. none of the above Q7, 8 and 9 is based on the following statement: If sin 39° = p, determine the following in terms of p: Question 7 sin 129° A. p2 1 B. 1 p2 C. B. 1 p2 C. B. 1 p2 C. 2 p. 1 p p2 Question 8 tan 321° A. p2 1 p p 1 p2 Question 9 sin 78° p2 1 A. p 2 Improve your Skills Question 1 Simplify without using a calculator, showing your working details: tan 60 cos 240 sin 310 sin 270 cos 220 sin 300 (6) Question 2 Consider the identity: sin A 1 cos A 2 1 cos A sin A sin A a.) Prove it! b.) Give all values of A 0;360 for which it is undefined. (5) (2) Question 3 Given that sin 23 g , express the following in terms of g: sin 203 b.) cos 23 c.) cos113 d.) tan 203 a.) (1) (2) (2) (2) Question 4 If cos10 t then determine cos340 in terms of t: (3) Question 5 Express cos 2x in terms of sin x . (2) Question 6 Solve the following equation for 0;180 : cos 4 cos 20 sin 4 sin 20 0.5 Question 7 Consider the following identity: a.) Prove it! sin 3x sin 7 x tan 5 x cos 3x cos 7 x Hint : 3x 5x 2x and 7 x 5x 2x b.) Hence or otherwise solve: sin 3x sin 7 x 1 for x 0;90 cos3x cos 7 x (6) (3) Question 8 Prove the following identities: 1 sin(45 x)sin(45 x) cos 2 x 2 a.) 2 1 sin 2 x cos x 1 sin 2 x sin x b.) (4) (3)