Sketch the graph of $y = - ext{sin} \, x$ for $0^ ext{o} < x \leq 360^ ext{o}$. - OCR - GCSE Maths - Question 16 - 2019 - Paper 6
Question 16
Sketch the graph of $y = - ext{sin} \, x$ for $0^ ext{o} < x \leq 360^ ext{o}$.
Worked Solution & Example Answer:Sketch the graph of $y = - ext{sin} \, x$ for $0^ ext{o} < x \leq 360^ ext{o}$. - OCR - GCSE Maths - Question 16 - 2019 - Paper 6
Step 1
Identify the Behavior of the Function
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Answer
The function y=−extsinx is the reflection of the sine wave across the x-axis. The standard sine function oscillates between -1 and 1, thus y=−extsinx will oscillate between -1 and 1.
Step 2
Determine Key Points
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Answer
The sine function has key points at intervals of 90exto, therefore the following key points for y=−extsinx are relevant:
At x=0exto, y=−extsin(0)=0.
At x=90exto, y=−extsin(90)=−1.
At x=180exto, y=−extsin(180)=0.
At x=270exto, y=−extsin(270)=1.
At x=360exto, y=−extsin(360)=0.
Step 3
Sketch the Graph
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Answer
To sketch the graph:
Plot the key points identified above on the Cartesian plane.
Connect these points with a smooth, continuous wave-like curve. Ensure the curve starts at (0,0), dips to (90,−1), returns to (180,0), rises to (270,1), and ends back at (360,0) to complete one cycle.
The approach creates a visual representation of the negative sine function across the specified interval.
