Here is the graph of $y = ext{sin}^3(x)$ for $-180 \leq x \leq 180$ - Edexcel - GCSE Maths - Question 18 - 2018 - Paper 1
Question 18
Here is the graph of $y = ext{sin}^3(x)$ for $-180 \leq x \leq 180$.
On the grid, sketch the graph of $y = ext{sin}^2(x) - 2$ for $-180 \leq x \leq 180$.
Worked Solution & Example Answer:Here is the graph of $y = ext{sin}^3(x)$ for $-180 \leq x \leq 180$ - Edexcel - GCSE Maths - Question 18 - 2018 - Paper 1
Step 1
Step 1: Understanding the Function
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Answer
The given function is y=extsin2(x)−2. The extsin2(x) function oscillates between 0 and 1. Therefore, the range of y=extsin2(x) is [0, 1]. By subtracting 2, the range of y=extsin2(x)−2 becomes [-2, -1].
Step 2
Step 2: Key Points and Intercepts
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Answer
To sketch the graph, identify key angles. For example, at x=0, y=extsin2(0)−2=0−2=−2; hence the point (0, -2) exists. Similarly, at x=90, y=extsin2(90)−2=1−2=−1, giving the point (90, -1). At x=−90, the same value holds due to sine's symmetry.
Step 3
Step 3: Sketching the Graph
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Answer
The graph will be a smooth curve that oscillates between the points steered by the above evaluations, remaining in the range of [-2, -1]. It will touch the line y=−2 at x=0 and reach y=−1 at x=90 and x=−90, with equal negative bumps around these points reflecting sinusoidal behavior.
