Here is a graph of $y = ext{sin} heta$ for $0 ext{ } heta ext{ } 360$ - Edexcel - GCSE Maths - Question 18 - 2021 - Paper 2
Question 18
Here is a graph of $y = ext{sin} heta$ for $0 ext{ } heta ext{ } 360$.
(a) Using this graph, find estimates of all four solutions of
$\text{sin} \theta = 0.6$... show full transcript
Worked Solution & Example Answer:Here is a graph of $y = ext{sin} heta$ for $0 ext{ } heta ext{ } 360$ - Edexcel - GCSE Maths - Question 18 - 2021 - Paper 2
Step 1
Using this graph, find estimates of all four solutions of sin θ = 0.6 for 0 ≤ θ ≤ 720
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Answer
To find the solutions of extsinθ=0.6 from the graph:
Identify the points where the graph intersects the line y=0.6.
From the graph, the first intersection occurs at approximately 37∘. The second solution, found in the first period (0≤θ<360), is approximately 143∘.
For the second period (360<θ≤720), the corresponding solutions will be:
Third solution: 397∘ (which is 360+37)
Fourth solution: 503∘ (which is 360+143)
Thus, the four solutions are approximately 37∘, 143∘, 397∘, and 503∘.
Step 2
Write down an equation of the reflected graph.
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Answer
The reflection of the graph of y=extsinθ in the x-axis is given by:
y=−sinθ
Step 3
On the grid, draw the graph of y = f(θ - 2)
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Answer
To graph y=f(θ−2):
Shift the graph of y=f(θ) to the right by 2 units.
For every point (x,y) on the original graph, the new points will be (x+2,y).
