The Illustrator arc tool is just beneath the live line segment in tools box. Click to use it to create a basic curved design in a variety of styles.
Press return or double click the icon. Unlike many, it has a nice preview (a small preview) and you can try out different designs using the settings in the preview, personally I generally just create the basic design on the art board and don't use the fixed length settings but they are useful for creating interesting shapes in combo with the slope.
The base x axis y axis is much as the little origin control to the right of the x-axis length. The type closed generates a closed path (though not a filled path) and the open generates your basic open shape that is not closed. The fill just adds the current fill color. The slope is great for creating the slope in either direction, as a dip or bump. 45 degrees is the best setting for a basic design.
You can add the shape as a filled closed object, set it to closed and apply it to the art board, Go to the fill and set the fill color.
Go to the window menu and appearance panel. Go to the panel with the shape selected and right side menu to add new fill as well as additional strokes. You can also keep that selected and then go to the effect menu and distort and transform and transform and set the scale to 90 / 90 as well as set the origin and create a new slight smaller arc inside the current one. You can then repeat this with different colors such as 80, 70, 60 etc. This can all be modified via the appearance panel.
You can add all kinds of designs but you can extend them further by using the width profiles as the top of the application as well as using the width and with that selected you can click anywhere along the design and resize the stroke at that point and create all kinds of unique artworks. If you want to use it as a fill, you will need to go to the object menu and expand it.
Select the shape and go to the stroke settings (stroke panel etc found via the window menu) or via the properties panel. You can set the dashed line to ON and then set the dash and gaps for the vector design. All kinds of magical designs can be created by using this and it works also in combination with width profiles etc
You can also use it to create shapes that can then be repeated using the object menu and repeat and radial. You can then modify the radius of the design along with the instances. You can change the repeat object by double clicking one of the instances. You can modify the design in countless ways by using curvature as well as direct selection and also any number of plugins such as PathScribe.
You can use it when you are in pattern moder. Create an design and then go to the object menu and pattern and make. You can then manipulate the design in numerous ways and create all kinds of pattern tiles saved in the swatches panels that can be used with selected paths such as creating amazing hex artwork using the vector
The vector created by this is a standard path and you can edit it in countless ways such as using the curvature to manipulate the points of the curve you can drag and re-position the points to create unique designs.
Go to the direct selection and then you can manipulate the curve in all kinds of ways by selecting one of the points and then you will see the direction handles appear. You can select the direction points and drag to a different position reshaping the curve. You can also click on the curve itself and reshape that without adding any new points to the design. Hold down the shift key to constrain the movement. Hold down the alt or option key while using the direct selection and you can also duplicate the path and reposition.
The design can be selected and warped using a number of different features such as the effects in the effect menu such as zigzag as well as the wrinkle / scallop etc in the toolbar as well as the powerful crystallize to add a lot of extra points to the line, which in turn can be manipulated by the direct selection.
You can add them to the current line such as blurring, zigzag etc. If you add any, go to the appearance panel to tweak them. You can make 100s of the lines by by selecting the path and then going to the effects and selecting distort and transform and transform and set the copies to 10 and set the shift / scale etc and move it.