Answer :
It seems there is an error in the function provided. The function `y = cos(x+)` is incomplete. There is an operator "+" followed by nothing, which makes the expression invalid as it does not specify what is to be added to `x` inside the cosine function.
To graph a cosine function, we need a complete and valid function, like `y = cos(x)` or `y = cos(x + c)` where 'c' is a constant or another variable that modifies the input to the cosine function.
Assuming that the "+" is a typographical error and you meant to write `y = cos(x)`, I will now explain how to graph this function assuming π = 3.14.
The graph of `y = cos(x)` is a wave that oscillates between 1 and -1, with a period of `2π` (approximately 6.28 when using 3.14 for π) and an amplitude of 1.
To graph the function `y = cos(x)`, you should follow these steps:
1. Draw the coordinate axes: Label the horizontal axis as 'x' and the vertical axis as 'y'.
2. Plot key points: Since cosine has a period of `2π`, you should mark points along the x-axis at intervals of π/2 (about 1.57), π, 3π/2, and 2π. At `x = 0`, `y = cos(0) = 1`, so the first point is (0, 1). At `x = π/2`, the cosine of π/2 is 0, so mark the point (π/2, 0). At `x = π`, `cos(π) = -1`, so mark (π, -1). At `x = 3π/2`, cosine is 0 again, and at `x = 2π`, `cos(2π) = 1`, closing one full cycle of the wave. Mark these points on the graph.
3. Draw the cosine wave: Using the points marked, draw the curve of the cosine function. The transition from one point to the next should be smooth and wave-like, with the curve reaching its maximum at `y = 1` and its minimum at `y = -1`.
4. Extend the graph: You can extend this wave to the left and right by continuing the pattern. To the left, the wave will pass through the points (−π/2, 0), (−π, 1), (−3π/2, 0), and (−2π, -1), and so on. To the right, continue beyond (2π, 1) to (5π/2, 0), (3π, -1), etc.
5. Label your graph: Add a title such as "Graph of y = cos(x)", and ensure everything is clearly marked, including the units on the axis.
Lastly, remember when graphing trigonometric functions, the x-axis is commonly represented in terms of π to show the cyclical nature of these functions.
To graph a cosine function, we need a complete and valid function, like `y = cos(x)` or `y = cos(x + c)` where 'c' is a constant or another variable that modifies the input to the cosine function.
Assuming that the "+" is a typographical error and you meant to write `y = cos(x)`, I will now explain how to graph this function assuming π = 3.14.
The graph of `y = cos(x)` is a wave that oscillates between 1 and -1, with a period of `2π` (approximately 6.28 when using 3.14 for π) and an amplitude of 1.
To graph the function `y = cos(x)`, you should follow these steps:
1. Draw the coordinate axes: Label the horizontal axis as 'x' and the vertical axis as 'y'.
2. Plot key points: Since cosine has a period of `2π`, you should mark points along the x-axis at intervals of π/2 (about 1.57), π, 3π/2, and 2π. At `x = 0`, `y = cos(0) = 1`, so the first point is (0, 1). At `x = π/2`, the cosine of π/2 is 0, so mark the point (π/2, 0). At `x = π`, `cos(π) = -1`, so mark (π, -1). At `x = 3π/2`, cosine is 0 again, and at `x = 2π`, `cos(2π) = 1`, closing one full cycle of the wave. Mark these points on the graph.
3. Draw the cosine wave: Using the points marked, draw the curve of the cosine function. The transition from one point to the next should be smooth and wave-like, with the curve reaching its maximum at `y = 1` and its minimum at `y = -1`.
4. Extend the graph: You can extend this wave to the left and right by continuing the pattern. To the left, the wave will pass through the points (−π/2, 0), (−π, 1), (−3π/2, 0), and (−2π, -1), and so on. To the right, continue beyond (2π, 1) to (5π/2, 0), (3π, -1), etc.
5. Label your graph: Add a title such as "Graph of y = cos(x)", and ensure everything is clearly marked, including the units on the axis.
Lastly, remember when graphing trigonometric functions, the x-axis is commonly represented in terms of π to show the cyclical nature of these functions.
