Curved lines are tricky to draw freehand, but the Pen tool in Adobe Photoshop generates curves of great accuracy. The curved lines are first drawn as paths and then a stroke is applied. Before applying the stroke, you adjust the work path created with the Pen tool until you are satisfied with the exact curvature of the line. The work path can be saved if you plan to reuse it later.
Open Adobe Photoshop and press "Ctrl-N" to create a blank canvas or "Ctrl-O" to open an existing image.
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Press "Ctrl-`" to display a grid overlay that is useful as guidelines.
Select the Pen tool from the tool menu and then select "Path" from the Options bar at the top of the screen.
Click a spot on the canvas to create the starting point of the curved line.
Click and hold a different spot on the canvas to select the end point of the curved line.
While still holding down the mouse button, drag the cursor downward to form an upward curve and vice versa. The further you drag the mouse up or down, the more severe the curve.
Select "Window" from the menu bar and then select "Paths" if the Paths panel is not visible.
Right-click the name of the path you created -- by default it is "Work Path" -- from the Paths panel and then select "Stroke Path" from the context menu. Select the type of tool that you want to use to create the curved line from the Tool drop-down list.
Click "OK" to create the curved line based on the settings for the tool that you have selected. Although the path is visible on your screen, it will not be visible in the saved document or when printed unless you apply a stroke to the path.