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Here is a graph of $y = ext{sin} heta$ for $0 ext{°} ext{≤} heta ext{≤} 360 ext{°}$ - Edexcel - GCSE Maths - Question 19 - 2021 - Paper 2

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Question 19

Here-is-a-graph-of-$y-=--ext{sin}--heta$-for-$0--ext{°}--ext{≤}--heta--ext{≤}-360--ext{°}$-Edexcel-GCSE Maths-Question 19-2021-Paper 2.png

Here is a graph of $y = ext{sin} heta$ for $0 ext{°} ext{≤} heta ext{≤} 360 ext{°}$. (a) Using this graph, find estimates of all four solutions of $\text{si... show full transcript

Worked Solution & Example Answer:Here is a graph of $y = ext{sin} heta$ for $0 ext{°} ext{≤} heta ext{≤} 360 ext{°}$ - Edexcel - GCSE Maths - Question 19 - 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

From the graph of y=extsinhetay = ext{sin} heta, we can observe the points where the curve intersects the line y=0.6y = 0.6. The approximate x-coordinates for the intersections in the interval 0ext°ext≤hetaext≤720ext°0 ext{°} ext{≤} heta ext{≤} 720 ext{°} are:

  1. heta1≈37ext° heta_1 \approx 37 ext{°}
  2. heta2≈143ext° heta_2 \approx 143 ext{°}
  3. heta3≈397ext° heta_3 \approx 397 ext{°}
  4. heta4≈503ext° heta_4 \approx 503 ext{°}

Step 2

Write down an equation of the reflected graph.

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Answer

The equation of the reflected graph in the xx-axis is given by: y=−sinθy = - \text{sin} \theta

Step 3

On the grid, draw the graph of y = f(θ - 2).

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Answer

To graph y=f(θ−2)y = f(\theta - 2), we need to shift the original graph of y=f(θ)y = f(\theta) to the right by 2 units. Begin by identifying key points from the original graph, then translate these points horizontally to create the new graph.

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