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i0Jq,.FF22222,FFFFTrig graphs sine and cosine: Math Analysis
This activity is intended for students to better understand transformations of graphing sine and cosine based on this equation: y = asin(bx c) d, where a = amplitude, b = period, c = the horizontal shift and d = vertical shift.
After the students have logged onto navigator and the teacher should go in to activity center. Use sin_graph.act to have the correct viewing window. Plot y = sin(x) or y = cos(x). To graph these by hand I use [0, 2pi], one period.
Ask the students these questions. They should be able construct an equation and graph it based on the information that the teacher gives. After information has been given out, each student should plot what he thinks is the right answer. After all students have contributed their answer, the teacher should graph the correct answer.
Some examples to use for this activity:
What would the graph look like if the amplitude and graph was lowered 3 units?
What would the graph look like if the graph was raised 4 units?
What would the graph look like if the graph had a period of pi?
What would the graph look like if it was shifted pi/2 to the right? What would the new end points be for one period of the graph?
What would the graph look like if it was shifted pi to the left? What would the new end points be for one period of the graph?
What would the graph look like if the period is 4pi and the amplitude is ?
What would the graph look like if the period is pi/2 shifted left pi/3 and has amplitude of 3? What would the new end points of one period of this graph?
Use the learning check activity to check for students learning of this topic.
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