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Unit 6 MCR 3U1 Lesson 5: Using Transformations to Sketch Graphs of Sinusoidal Functions Vertical Translations The graphs of y sin x c and y cos x c can be summarized as follows. If c 0 , a vertical translation of c units upwards occurs. If c 0 , a vertical translation of c units downwards occurs. Vertical translations affect the range of the function. The equation of the axis is y c . Horizontal Translations For trigonometric functions, a horizontal translation is called the phase shift. The graphs of y sin( x d ) and y cos( x d ) can be summarized as follows. If d 0 , a horizontal translation of d units to the left occurs. If d 0 , a horizontal translation of d units to the right occurs. Reflections If a 0 , then the function is reflected in the x-axis. If k 0 , then the function is reflected in the y-axis. Example 1: For each of the following: i) Describe the transformations that occur. ii) Sketch one cycle of the graph. iii) State the period, amplitude, maximum, minimum and domain and range of one cycle for each function. a) y 2 cos x 2 Unit 6 b) y 0.5 sin( x 90) MCR 3U1 c) y 2 sin( 0.5 x 90) 1 Example 2: Determine the equation of the sine function shown.