Create the letter M in desmos. It must be a BLOCK M and you can use the following:
Polynomial (degree 3 and higher), Rational, Trigonometric and Logarithmic functions. You're also open to use square root functions, exponential functions, and circles.

Make sure that the top of the "M" does not exceed y = 13 and the bottom does not go below y = 1.5 (use this to figure out the size of the M itself).

You want a series of functions and their transformations that will develop a graph of a block capital letter "M", using trig functions.

Approach

The block letter M consists mainly of straight lines. To approximate a straight line, we have elected to use the portion of the sine function in the interval [-π/3, π/3] where it is approximately straight, but shows a hint of the sine function.

First, we created a function that moves that segment of the sine function so it is defined between the points (0, 0) and (1, 1). This makes scaling relatively easy.

Then, we created a function that draws that segment between coordinates (a, b) and (c, d).

Letter M

We used this second function to draw segments between the points we chose for the outline of the left half of the letter.

Finally, we created the right half of the letter by reflecting those functions over the vertical line of symmetry (at x = 4.7). The end result is shown in the first attachment. The function and segment definitions not shown in the first attachment are shown in the second attachment. The f( ) in the Reflection section fills in the horizontal segment between the two halves of the letter.

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Additional comment

Appending this identifier to the Desmos URL will give you the graph and function definitions we show here. This should eliminate the need to type them, if the result here is suitable.

We have used 13 function definitions that need to be changed if you desire to move the letter to different coordinates or scale it. You could combine these into two piecewise functions (one for the top, one for the bottom), so that translation or scaling could be done more easily.

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