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Here is a graph of y = sin x° for 0 ≤ x < 360 (a) Using this graph, find estimates of all four solutions of sin x° = 0.6 for 0 ≤ x ≤ 720 - Edexcel - GCSE Maths - Question 19 - 2021 - Paper 2
Question 19
Here is a graph of y = sin x° for 0 ≤ x < 360 (a) Using this graph, find estimates of all four solutions of sin x° = 0.6 for 0 ≤ x ≤ 720. The graph of y = sin x° i... show full transcript
Worked Solution & Example Answer:Here is a graph of y = sin x° for 0 ≤ x < 360 (a) Using this graph, find estimates of all four solutions of sin x° = 0.6 for 0 ≤ x ≤ 720 - Edexcel - GCSE Maths - Question 19 - 2021 - Paper 2
Step 1
a) Using this graph, find estimates of all four solutions of sin x° = 0.6 for 0 ≤ x ≤ 720.
Answer
To find the solutions to the equation , refer to the graph provided:
- Identify where the graph intersects the horizontal line at y = 0.6.
- From the graph, the intersections occur at approximately:
- Solution 1: x = 37°
- Solution 2: x = 143°
- Since the sine function is periodic, we can calculate additional solutions for the interval 0 ≤ x ≤ 720:
- Solution 3: x = 360° + 37° = 397°
- Solution 4: x = 360° + 143° = 503°
Thus, the four solutions are approximately: 37°, 143°, 397°, and 503°.
Step 2
Step 3
c) On the grid, draw the graph of y = f(x - 2)
Answer
To draw the graph of y = f(x - 2), you need to horizontally translate the original graph y = f(x) by 2 units to the right. This means every point (x, f(x)) on the original graph becomes (x + 2, f(x)). Ensure that key points and features (like intercepts and turning points) are reflected in the new graph.