Mathematics Higher Level Robert Joinson

©Sumbooks 2002Higher Level60. Graphs of Sines, Cosines and Tangents1. The diagram shows the graph of y =sin xa) Sketch this into your book and mark on it theapproximate solutions to the equationsin x° = – 0.5 where x lies between 0° and360° .b) Calculate accurately the solution to theequation sin x° = – 0.5 where x lies between0° and 360° .1.000°–1.0180° 360°2. a) Draw a graph of y = 2sin x° + 1 for0° ≤ x ≤180°using a scale of 2cm for 1 unit on the y axis and 2cm for 30°b) From your diagram, calculate the values of x which satisfy the equation2sin x° + 1 = 2.5 for 0° ≤ x ≤180°.on the x axis.3. a) Sketch the graph of y = cos x for 0° ≤ x ≤360°.b) Show on the diagram the approximate locations of the solutions to the equationcos x = – 0.5 for 0° ≤ x ≤360°.4. a) Draw the graph of y = 3cos x + 2 for 0° ≤ x ≤360°. Use a scale of 2cm for 1 unit onthe y axis and 4cm for 90° on the x axis.b) From the graph, calculate the solutions to the equation 3cos x° + 2 = 3 for0° ≤ x ≤360°.5. The diagram on the right shows a sketch ofy= tan x for 0° ≤ x ≤360°. From the graph10determine the approximate solutions to the equationtan x = 4 for 0° ≤ x ≤360°.56. a) Sketch the graph of y = tan x + 2 , for0° ≤ x ≤360°. Indicate on the graph theapproximate location of the solution to theequation tan x + 2 = 0 for 0° ≤ x ≤360°.00˚–5180˚360˚b) Sketch the graph of y = 3tanx on the sameaxis as y = tan x for 0° ≤ x ≤180°clearlyshowing the difference between the twographs.–107. a) Sketch the graph of y = 2tan x – 1 for 0° ≤ x ≤360°.b) Indicate on the graph the approximate location of the solution to the equation2tan x – 1 = 2 for 0° ≤ x ≤360°.