+ Experiment with the sliders below to figure out how each 66 component affects the graph. V y=a cos(b(x + h))+k O a= 2.1 -4 y = 2,1 cosN.13(x + -2.2))+0.1 O b= 1.13 O h= -2.2 -10 10 fi/2 S/2 O k= 0.1 -10 10
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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![### Task 4: Experiment with Cosine
In this task, you'll explore how different parameters affect the graph of a cosine function. Experiment with the sliders to see the variations in real-time.
#### Function and Sliders
The function under investigation is:
\[ y = a \cos \left( b(x + h) \right) + k \]
You can manipulate the following parameters using the sliders:
- \( a = 2.1 \)
- \( b = 1.13 \)
- \( h = -2.2 \)
- \( k = 0.1 \)
#### Graph Explanation
The graph displays the effect of these parameters on the cosine function.
1. **Amplitude** (\( a \)): The slider for \( a \) changes the vertical stretch or compression of the cosine wave. The amplitude \( a \) is currently set at 2.1, meaning the graph will have a peak value of 2.1 and a trough value of -2.1.
2. **Frequency** (\( b \)): The slider for \( b \) adjusts the horizontal stretch or compression, which changes the frequency of the wave. A \( b \) value of 1.13 results in a slightly stretched wave compared to the standard cosine function.
3. **Horizontal Shift** (\( h \)): Adjusting \( h \) translates the graph horizontally. With \( h \) set to -2.2, the function shifts 2.2 units to the left.
4. **Vertical Shift** (\( k \)): The \( k \) value moves the entire function up or down. A \( k \) value of 0.1 shifts the graph slightly upwards.
#### Visualization
In the graph:
- The red curve represents the cosine function with the given parameters: \( y = 2.1 \cos(1.13(x + (-2.2))) + 0.1 \).
- The green dashed line shows a standard cosine function for comparison.
You can observe how altering each parameter with the sliders impacts the graph's shape and position. Try changing the values to understand better how cosine function parameters influence its graph.
Explore and enjoy your experiment with cosines!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ce901d6-1005-4fae-945e-8fe9887caefc%2F03ce6770-c7ad-40c0-906d-634e13410aa1%2Fhoy41xp_processed.png&w=3840&q=75)
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