TRIGONOMETRIC RATIOS. NO HANDWRITTEN ANSWERS

1. Complete the table below by filling in the blank spaces. 30' 60' 90" 120" 150" 180" 210" 240" 270" 300" 330" 360" Cos x 1.00 0.50 -0.87 -0.87 2cos//zx 2.00 1.93 0.50 (2mks) On the grid provided, using a scale of 1 cm to represent 30" on the horizontal axis and 4cm to represent 1 unit on the vertical axis draw the graph of y = cos x" and y = 2 cos 1/2 x". (4mks) (a) State the period and amplitude of y = 2 cos V/2 x" (2mks) (b) Use your graph to solve the equation 2 cos 1/2 x - cos x = 0. (2mks) 2. a) Complete the table below by filling in the blank spaces X -90 -75 -60 -45 30 - 15 15 30 45 60 75 90 30082x-1 -40 -3.6 -1.0 0.5 1.6 1.6 0.5 -2.5 -3.6 -4.0 2sin (2x+30) -1.0 -1.73 -1.73 -1.0 1.73 2.0 1.0 0 -1.0 b) On the grid provided, draw on the same set of axes the graphs of y = 3cos 2x -1 and y =2sin(2x +30" )for-90" x $90". Using a scale o 1 cm for 150 on axis and 2 cm for I unit on the y-axis (5mks) c) State the period of y = 3cos 2x -1 (1mk) d) Solve the equation 2sin(2x+30" )-3cos 2x +1 =0 (2mks) 3. Complete the table below by filling in the blank spaces. 30 60 90 120% 150 180 210 240- 270 300 330 360 Cos x 1.00 0.5 -0.87 -0.87. 2 cos 1/ x 2.00 1.93 0.52 -1.00 -2.00 Using the scale 1 cm to represent 30" on the horizontal axis and 4cm to represent 1 unit on the vertical axis, draw on the grid provided, the graph of y = cos x" and y = 2 cos 1/2 x" a) Find the period and amplitude of y = 2cos V/2 x" (2mks) b) Describe the transformation that maps the graph of y = Cos x" on the graph of y = 2 cos 1/2 X". (2mks) 4. The table below gives some values of y = sin 2x and y = 2 cox is the range given. (a) Complete X' -225 -180 -135 -90 -45 0 45 90 135 180 225 y - sin 2x -1.0 1.0 0 -1.0 1.0 y = 2cos x 1-1.4 -1.4 2.0 -1.4 -1.4