Comparing Bike Pedal Motion to Sine Function Graph
When riding a bike and pumping the pedals at a constant rate, the graph of the height of one foot follows a pattern similar to a sine function. Understanding the relationship between the two graphs can help in visualizing trigonometric functions and their translations.
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Presentation Transcript
Think about riding a bike and pumping the pedals at a constant rate of one revolution each second. How does the graph of the height of one of your feet compare with the graph of a sine function?
13-7 Translating Trigonometric Functions Today s Objective: I can write and graph a trigonometric functions.
Translating Functions Vertical ?(?) Horizontal ?(?) Translate h units horizontally ? ? + ? ?(? ) Translate k units vertically Midline: y = k Phase Shift ? = ??? ? ? ? = ??? ? + ? ? h=? ? ? = ? ? = ???(?) ? = ???(?)
Family of Trigonometric Functions Parent Functions Transformed Function ? = ? sin?(? ?) + ? ? = ? cos?(? ?) + ? ? = sin? ? = cos? ? = Amplitude: Vertical stretch or shrink 2? ? =Phase shift: Horizontal shift = Period ? =Vertical shift : y = k is midline
Graph each function on interval from 0 to 2 ? = sin ? +? 2 Amplitude: Midline: 1 2 ? = 2 Period: 2? Left ? Phase Shift: 2 Graphing: 1. Sketch in Midline (y = k) 2. Graph beginning point with phase shift. 3. Graph remaining four points.
Graph each function on interval from 0 to 2 ? = 2cos ? ? 3 Amplitude: Midline: 2 + 1 ? = 1 Period: 2? Right ? Phase Shift: 3 Graphing: 1. Sketch in Midline (y = k) 2. Graph beginning point with phase shift. 3. Graph remaining four points.
Write a sine and cosine function for the graph. ? = ? sin?(? ?) + ? ? ? ? = sin (? ) + ? ? ? ? = ? cos?(? ?) + ? ?? ? ? = cos (? ? ) + ? ?
Graph each function on interval from 0 to 2 ? = 3sin2 ? ? 6 Amplitude: Midline: 3 + 2 ? = 2 Period: ? Right ? Phase Shift: 6 Graphing: 1. Sketch in Midline (y = k) 2. Graph beginning point with phase shift. 3. Graph remaining four points.
