PRINTABLE VERSION Quiz 11 Question 1 Use the appropriate angle-sum formula to simplify the following expression: cos(5x) cos(4x) sin(5x) sin(4x) . a) cos(9x) b) sin(9x) c) cos(x) d) cos(20x) e) sin(x) f) None of the above. Question 2 Use the appropriate angle-sum formula to simplify the following expression: 2 2 cos( ) + sin sin( ) . ( 3 ) ( 3 ) 8 8 cos 13 ( 24 ) a) sin b) 13 cos ( 24 ) c) cos( d) 19 sin ( 24 ) e) 19 cos ( 24 ) 12 ) f) None of the above. Question 3 Given cos(x) = 8 3 with 0 < x < 90 and cos(y) = with 270 < y < 360 find cos(x + y) . 17 5 a) 13 85 b) c) 84 85 d) 91 85 e) 77 85 f) None of the above. 36 85 Question 4 Given sin(x) = 8 3 with 0 < x < 90 , and sin(y) = with 0 < y < 90 . Find sin(x + y) . 9 5 a) 179 45 b) 17 32 + 3 45 c) 32 3 17 45 d) 16 2 + 9 7 45 e) 8 2 + 3 45 f) None of the above. Question 5 Find cos( using the sum or difference formulas. 12 ) a) 6 2 b) 2 + 6 4 c) 2 + 6 4 d) 2 + 6 4 e) 3 f) None of the above. Question 6 Use the appropriate angle-sum formula to simplify and evaluate: sin(95 ) cos(35 ) sin(35 ) cos(95 ) . a) 3 2 b) 1 + 3 2 c) 3 2 d) e) 1 2 f) None of the above. 1 2 Question 7 Given tan(A) = 10 and tan(B) = 5 , find the value of tan(A B) . a) 5 49 b) 15 49 c) 50 51 d) 5 51 e) 5 17 f) None of the above. Question 8 Find the value of cos(105 ) using sum and difference formulas. a) 6 + 2 4 b) 6 2 4 c) 3 8 d) 6 + 2 4 e) f) None of the above. 2 6 2 4 Question 9 Given is an acute angle such that sin() = 4 5 . Find the value of tan + . 5 ( 4 ) a) 1 7 b) 7 c) 4 d) 1 e) 1 f) None of the above. Question 10 ( Consider the function f (x) = sin x + 7 7 sin x over the interval [0, 2). Simplify the ( 4 ) 4 ) formula of this function and find its minimum value on this interval. a) 2 b) 2 2 c) 1 d) 3 e) f) None of the above. 1 2