I don't understand this. can you please tell how you got each answer?
describe how the graph of each function is related to a basic trigonometric graph.
1. y= 1/2cos x
2. y= 2cos x+1
3. y= sin x-4
4. y= sin(x-4)
5. y= sin(3x)
6. y= cos(1/2x)
7. y= -cos x
8. y= -cos x+2
9. y= -4sinx
10. y= 4sin(-x)
Pleeease help! thank you!
In google type:
functions graphs online
When you see list of results click on: rechneronline.de/function-graphs/
When page be open in blue rectangle type:
1/2cos(x)
And click option: Draw
then type :
2cos(x)+1 OR 2cos (x+1)
And click option: Draw
etc.
You must write correct expresions.
thank you!
how does that tell how the graph of the function is related to a basic trigonometric graph?
Sure! I can help you understand how each graph is related to a basic trigonometric graph. Let's go through each function one by one:
1. y = (1/2)cos x
In this function, the coefficient of cos x is 1/2, which means the amplitude of the cosine function is reduced by half compared to the basic cosine graph. The graph will oscillate up and down centered around the x-axis, but the highest point and the lowest point will be half of what they would be in the basic graph.
2. y = 2cos x + 1
In this function, the coefficient of cos x is 2, which means the amplitude of the cosine function is doubled compared to the basic cosine graph. The graph will oscillate up and down centered around the x-axis, but the highest point and the lowest point will be twice of what they would be in the basic graph. Additionally, the entire graph will be shifted upward by 1 unit.
3. y = sin x - 4
In this function, the whole sine graph is shifted downward by 4 units compared to the basic sine graph. The graph will oscillate up and down centered around the x-axis, but the highest point and the lowest point will be shifted downward by 4 units.
4. y = sin(x - 4)
In this function, the entire sine graph is shifted horizontally by 4 units to the right compared to the basic sine graph. The graph will still oscillate up and down, but the starting point will now be at x = 4.
5. y = sin(3x)
In this function, the x-values are multiplied by 3 compared to the basic sine graph, causing the graph to oscillate three times faster. The graph will still oscillate up and down, but the period of the oscillations will become one-third of the basic sine graph.
6. y = cos(1/2x)
In this function, the x-values are divided by 2 compared to the basic cosine graph, causing the graph to oscillate twice as slowly. The graph will still oscillate up and down, but the period of the oscillations will become twice as long as the basic cosine graph.
7. y = -cos x
In this function, the entire cosine graph is reflected vertically. The graph will still oscillate up and down, but it will be reflected across the x-axis compared to the basic cosine graph.
8. y = -cos x + 2
In this function, the entire cosine graph is reflected vertically and shifted upward by 2 units compared to the basic cosine graph.
9. y = -4sin x
In this function, the entire sine graph is reflected vertically and amplified by a factor of 4 compared to the basic sine graph. The graph will still oscillate up and down, but the highest point and the lowest point will be four times what they would be in the basic sine graph.
10. y = 4sin(-x)
In this function, the entire sine graph is reflected horizontally and amplified by a factor of 4 compared to the basic sine graph. The graph will still oscillate up and down, but the highest point and the lowest point will be four times what they would be in the basic sine graph. Additionally, the entire graph will be reflected across the y-axis.
I hope this explanation helps you understand how each function is related to the basic trigonometric graph! Let me know if you have any more questions.