# Graphing of Cosine/Logarithm Function

• Malinn
In summary: This type of graph is commonly known as a "logcos" graph. In summary, the graph you are looking for is a combination of a cosine graph and a logarithmic graph, also known as a "logcos" graph. To graph this equation, enter it into your Texas Instruments calculator and it will automatically combine the two graphs together.
Malinn
I have been given a graph to sketch.
The original graph was:
T= 20-4cos(pi(x-1)/12)
I think I understand how to graph this , but later on they change it to this:
T= 20-loge(x) 4cos(pi(x-1)/12)

What type of graph is that? I don't even know if it exists, as I can't find anything in the textbook. I thought maybe, it would just be the "cos" part of the equation, but that doesn't work as that is the same as the original equation.
I know it must follow the same shape as a log graph would because it asks you to do this after sketching the second graph:

If the cycle starts at midnight Sunday, what day(s) will the temperature of the pool be more than 24.5 degrees celcius? (Just days not times)

This means it has to be a log shaped graph as if it was just the T= 20-4cos(pi(x-1)/12) then the temperature would never reach 24.5 degrees celcius (as themaximum value is 24)

So could someone please tell me how to graph this T= 20-loge(x) 4cos(pi(x-1)/12)? I have a "Texas Instruments Ti-nspire CAS" if that helps
Thanks alot.

The graph you are looking for is a combination of a cosine graph and a logarithmic graph. To graph this equation with your Texas Instruments calculator, simply enter the formula as it is written into the graphing calculator. The calculator will automatically combine the two graphs together to create the desired graph.

## 1. What is the purpose of graphing the cosine function?

The cosine function is a mathematical function that describes the relationship between the angles and sides of a right triangle. Graphing this function can help visualize this relationship and better understand its properties and behavior.

## 2. How do you graph a cosine function?

To graph a cosine function, you will need to plot points on a coordinate plane using values from the function's domain and range. The domain of the cosine function is all real numbers, and the range is from -1 to 1. You can also use a graphing calculator or software to create a more accurate and precise graph.

## 3. What does the graph of a cosine function look like?

The graph of a cosine function is a smooth, wavy curve that repeats itself indefinitely. It starts at the maximum value of 1, then decreases to the minimum value of -1, and then increases back to 1, creating a continuous cycle. The graph can also be shifted horizontally or vertically depending on the values of the function's parameters.

## 4. What is the purpose of graphing the logarithm function?

The logarithm function is the inverse of the exponential function and is used to solve equations involving exponential growth or decay. Graphing this function can help visualize the behavior of exponential functions and their inverse relationships, which are essential in many areas of mathematics and science.

## 5. How do you graph a logarithm function?

To graph a logarithm function, you will need to plot points on a coordinate plane using values from the function's domain and range. The domain of the logarithm function is all positive real numbers, and the range is all real numbers. The graph will have a vertical asymptote at x = 0, and the curve will approach but never touch the y-axis. You can also use a graphing calculator or software to create a more accurate and precise graph.

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