g10-07-09 · Core topics
Amplitude and a reflected wave
Does a negative coefficient mean a negative amplitude?
1 MIN · PREDICT ON PAPER
Compare the ranges of2sinx,−2sinx and0sinx.
Discuss or write first. No typed answer is required to continue.
The grey reference is sinx; compare one parameter at a time.
2 MIN · EXPLAIN AND REVISE
Which condition does your claim need?
Compare at least two cases. Write a reason, then check the explanation together.
Reveal explanation and conditions
For A sinx, the range is[−|A|,|A|]. Negative A reflects the wave; its amplitude is |A|. A=0 gives a constant.
Conditions: For a nonconstant sine wave A≠0. The zero case has range{0} and no least positive period.
Mathematical justification: Since −1≤sinx≤1 and both bounds are attained, multiplication by A gives the stated range, reversing order when A<0.
1 MIN · EXIT CHECK
State the amplitude and range of−3sinx.
Check after answering
Amplitude3; range[−3,3].
Teacher guidance and extension
Before: Angles, coordinates and basic function graphs.
Ask: Which quantity records reflection and which records size?
Watch for: Calling the amplitude−2 or treating A=0 as an ordinary oscillation.
Challenge: Compare A sinx and |A|sinx when A<0.
Suggested timing: predict 1 min, compare 3 min, explain 2 min, exit check 1 min. Observations can suggest a claim; they do not prove it for every input.
Optional local notebook
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