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Copy and complete the table of values for y = 3 cos x, 30° <= x <= 330°. Using a scale of 2 cm to 30° on the x-axis and 2 cm to 1 unit on the y-axis, draw the graph of y = 3 cos x for 30° <= x <= 330°. Use the graph to: (i) solve 3 cos x = 0; (ii) find the minimum point.
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2 partsUse the left and right arrow keys to trace the curve, up and down to jump between key points, and plus and minus to zoom.
| Point | x | y |
|---|---|---|
| x-intercept | 90° | 0 |
| Minimum | 180° | −3 |
| x-intercept | 270° | 0 |
Step-by-step solution
3 stepsHere's the continuation of Question 6, focusing on parts (c)(i) and (c)(ii).
Part 6
The function is for .
Part c(i)
solve ;
Use your graph to
Understand the equation .
This equation is equivalent to on the graph of . We need to find the values of where the graph intersects the x-axis.
Identify the x-intercepts from the table or graph.
From the table of values (or by looking at the graph you would draw), when and .
The solutions for are .
Part c(ii)
find the minimum point.
Identify the minimum value of and its corresponding from the table or graph.
The cosine function has a minimum value of . For , the minimum value will be .
This minimum occurs when , which happens at within the given range.
From the table, at , . This is the lowest point on the graph.
The minimum point is .
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