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Trig Identities Sum and Difference Page 1 of 4 Teacher: Mrs. Russolello Name: ____________________________________ Sum and Differences Identities Practice 9-4 1. 5. Express sin 75° cos 15° cos 75° sin 15° as a single The expression tan (180° + x) is equivalent to trigonometric function of a positive acute angle. 1. cot x 3. -cot x 1. cos 60° 2. tan x 4. -tan x 2. cos 85° -------------3. sin 60° 4. sin 85° 6. -------------- If tan A = 8 and tan B = 2. The expression cos 80° cos 20° equivalent to 1. 2. 3. 4. sin 80° sin 20° is cos 60° cos 100° sin 100° sin 60° (A + B)? 1. 4/3 2. 17/10 3. -15/6 4. -17/6 -------------- 7. -------------- 3. The expression sin 50° cos 40° + cos 50° sin 40° is equivalent to 1. 2. 3. 4. , what is the value of tan The value of cos 75° cos 15° sin 75° sin 15° is 1. 1 2. 3. sin 10° cos 10° sin 90° cos 90° 4. 0 --------------------------- 4. The expression sin (180° 1. sin x 2. cos x x) is equivalent to 3. -sin x 4. -cos x -------------- http://castlelearning.com/review/teacher/AssignmentPrinting.aspx 3/15/2012 Trig Identities Sum and Difference Page 2 of 4 8. 11. Since sin 75° = sin (30° + 45°), then sin 75° equals Find m in the interval 180° 270° that satisfies the equation 2cos + 1 = 0. 1. 210° 2. 235° 3. 240° 4. 260° -------------- 12. 180°, find the value of In the interval 90° satisfies the equation 2 sin 1 = 0. -------------- 1. 30° 2. 120° 9. that 3. 150° 4. 175° -------------- If A and B are positive acute angles, sin A = cos B = , and 13. , what is the value of sin (A + B)? If f (x) = sin2 x + cos2 x, find f ( ). 1. 1. 1 2. 2 2. 3. 3. 4. 0 -------------- 4. 14. -------------- 10. The expression cos 40° cos 10° + sin 40° sin 10° is equivalent to 1. cos 30° 2. cos 50° 3. sin 30° 4. sin 50° Which expression is equivalent to sin 22° cos 18° + cos 22° sin 18°? 1. 2. 3. 4. sin 4° cos 4° sin 40° cos 40° -------------- -------------- http://castlelearning.com/review/teacher/AssignmentPrinting.aspx 3/15/2012 Trig Identities Sum and Difference 15. The expression cos 1. 2. 3. 4. (sec 1 sin sin2 -cos2 Page 3 of 4 19. An architect is using a computer program to design cos ) is equivalent to the entrance of a railroad tunnel. The outline of the opening is modeled by the function f(x) = 8 sin x + 2, in the interval 0 x , where x is expressed in radians. (a) Solve algebraically for all values of x in the interval 0 x , where the height of the opening, f (x), is 6. Express your answers in terms of and in increasing order -------------- 16. Express sin 150° as a function of a positive acute angle. 1. 2. 3. 4. sin 30° cos 30° sin 60° -cos 60° Answer: and (b) If the x-axis represents the base of the tunnel, what is the maximum height of the entrance of the tunnel? Answer: units -------------- -------------- 17. If cos x = 12/13 and sin y = 4/5, then sin (x equals 1. 72/65 2. 56/65 y) 3. -16/65 4. -33/65 -------------- 18. What is the total number of solutions for the equation 3 tan2 A + tan A 2 = 0 in the interval 0 A ? 1. 2. 3. 4. 5. 1 2 3 4 0 -------------- http://castlelearning.com/review/teacher/AssignmentPrinting.aspx 3/15/2012 Trig Identities Sum and Difference Page 4 of 4 Answer Key for Trig Identities Sum and Difference 1. 3 2. 2 3. 3 4. 1 5. 2 6. 4 7. 4 8. 4 9. 1 10. 1 11. 3 12. 3 13. 1 14. 3 15. 3 16. 1 17. 4 18. 2 19. 1/6, 5/6, 10 http://castlelearning.com/review/teacher/AssignmentPrinting.aspx 3/15/2012