Trigonometric Graphing and Shifts Explained
Explore the concepts of determining period, amplitude, vertical and horizontal shifts in trigonometric functions. Learn how to identify and graph functions with various shifts.
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Presentation Transcript
Warm Up: Determine the period and amplitude of the function. Then, graph it! y = -9cos(2x)
MORE TRIGONOMETRIC GRAPHING
Lets shift! https://www.youtube.com/watch?v=BQ4QzTc G90g https://www.youtube.com/watch?v=zjSgkoaL _5A
Recall from yesterday: y = asin(bx) y = acos(bx) Amplitude of the graph = a Period of the graph = b 2
Vertical Shift (k) y = asin(b(x - c)) + d y = acos(b(x c)) + d When a graph moves up or down, it is called a vertical shift. d tells us which direction and how far to shift.
Example 1: State the direction and distance that each function has shifted. 1. y = cos(x) 3 2. y = sin(x) 2 3. y = sin(x) + 4 4. y = cos(x) +
Phase Shift (h) y = asin(b(x - h)) y = acos(b(x - h)) When a graph shifts left or right, it is called a phase shift. h tells us the direction and how far to shift. Note that h is subtracted, so go the opposite direction that you would assume.
Example 2: State the direction and distance that each function has shifted. 1. y = sin(2(x + )) 2. y = cos(x ) 3 3. y = cos(x + ) 4 3 4. y = sin(x ) 2
Putting it all together! y = asin(b(x c)) + d y = acos(b(x c)) + d Amplitude of the graph = a Period of the graph = 2 b Horizontal translation = c (note: opposite direction) Vertical translation = d
