UNIT – TEST Student name: _ Knowledge Application Communication Thinking Total /15 _/15 _/7 _/13 /50 Multiple Choice Identify the choice that best completes the statement or answers the question Determine the value of a b to the nearest degree if c d Determine the corresponding reciprocal ratio that corresponds to a c b d Determine the exact value of a b (K: /15) c d For the angle moving counter-clockwise in standard position, determine which primary trigonometric ratio is positive a sine c tangent b cosine d none are positive Angle 1) 2) 3) 4) a 1) b 2) lies in quadrant Without using a calculator, determine which ratio is valid c 3) d 4) Given a b , determine which of the following is an equivalent expression c d A triangular plot of land is enclosed by a fence One side of the fence is 40.1 m long with an opposite angle of An adjacent side of the fence is 37.7 m long with an opposite angle of Determine to the nearest degree a c b d Order the following waves according to the length of their periods, from least to greatest y Wave C Wave A 1 –1 10 11 12 13 x –2 Wave B –3 –4 a Wave B, Wave A, Wave C b Wave C, Wave A, Wave B If a b c Wave C, Wave B, Wave A d Wave B, Wave C, Wave A , determine c d 10 Determine the amplitude of the function a b c d 11 Determine the period of the function a b c d 12 Determine the period of graph A and graph B y A –5 –4 –3 –2 –1 –1 x –2 –3 –4 –5 B a A: 6; B: b A: 6; B: c A: 5; B: d A: 5; B: 13 Without graphing, determine the equation of the axis of the function a c b d 14 State the order of transformations for the function a horizontal transformation left ; vertical stretch by a factor of 0.125 b horizontal transformation left ; vertical compression by a factor of 0.125 c horizontal transformation right ; vertical stretch by a factor of d horizontal transformation right ; vertical compression by a factor of 15 Which of the following does not make sense? a period of b vertical stretch by a factor of 0.005 c amplitude of d horizontal translation units left Question # Answer Question # Answer 10 11 12 13 14 15 Short Answer y = − sin ( x − 22.5°) − 2 16 For the function , State the transformations, in the order you would apply them (C: /3) _ _ 17 Determine one value for which is true and one value for which it is not true (C: /2) 18 If you are given sides of a triangle, how can you find the measure of its angles? (C: /2) Problems 19 Fill in the following table for y = 5cos (3x + 180°) + and sketch cycles of the function (A: /8) Period Amp axis max Phase Shif 20 A scientist records the motion of a particle where d is the distance in mm and t is the time in seconds A graph of that motion is shown below (A: /4) a)What is the period of one complete cycle? Domain Range b) What is the range of this function? c) Determine the amplitude d) If the particle can survive for twenty complete cycles before deteriorating, determine the domain of the function 21 How many triangles can you make if in o ∆XYZ ∠Y = 42.6 , , y = 6.9 m, z = 9.7 m? (A: _/3) 22 Prove the following identity: a) 23 (T: _/4) cos θ − sin2 θ = − tan θ cos θ + sinθ cos θ The Ferris wheel at a carnival has a diameter of 10 m and rotates once every 40 seconds The bottom of the wheel is 2m above the ground Draw a diagram to show a rider’s height above the ground during ride, starting at the lowest position (T: /4) a find the equation of the sine function that gives a rider’s height above the ground, in meters, as a function of the time, in seconds (T: /2) Equation: b Suppose the Ferris wheel rotates every 10 seconds Adjust your equation in part a) to reflect this new situation (T: /1) Equation: c) Using the same situation as part a, model the rider’s height using a cosine function Equation: (T: /2) ... of transformations for the function a horizontal transformation left ; vertical stretch by a factor of 0.1 25 b horizontal transformation left ; vertical compression by a factor of 0.1 25 c horizontal... 0.0 05 c amplitude of d horizontal translation units left Question # Answer Question # Answer 10 11 12 13 14 15 Short Answer y = − sin ( x − 22 .5? ?) − 2 16 For the function , State the transformations,... c d 12 Determine the period of graph A and graph B y A ? ?5 –4 –3 –2 –1 –1 x –2 –3 –4 ? ?5 B a A: 6; B: b A: 6; B: c A: 5; B: d A: 5; B: 13 Without graphing, determine the equation of the