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Lesson 6.5
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Jump Start
Swinging in her car on a Ferris wheel while waiting for the last car to load, Anahita was thinking about her friends in her
math class. "I'm going to sketch a graph of my ride as soon as I get off, so I can remember to tell my friends all of the detail
of my ride."
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This is the graph Anahita made after exiting the ride.
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Discussion:
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Key features of the sine graph:
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Midline: the horizontal line through the middle of the graph.
Amplitude: the distance from the midline to the maximum or minimum points on the graph.
Period: the interval of the domain before the graph repeats itself.
Quick-graph points: beginning, middle, end of one revolution; maximum, minimum.
Shape of graph: Smooth curve, steeper at the points on the midline, more rounded at the maximum and minimum.
Graph this Function Equation: h(t)=30+25sin(181)
Step 1. Identify the midline (D), amplitude (A) and B = (300) from the function equation.
360°
Step 2. Calculate the Period: Period ==
18
period
Step 3. Identify Key Points:
maximum point: y = D+A=
minimum point: y = D-A=
Determine the maximum and minimum points. For a sine function, the maximum occurs at
y=D+A and the minimum at y-D-A. For a cosine function, the maximum occurs at y-D+A and the minimum at y=D-
Step 4. Plot Key Points:
a. Start by plotting the midline.
b. Identify other key points by dividing the period into 4 equal intervals.