Using expository text and examples available in 10 college textbooks we identify two conceptions of angles, trigonometric functions, and inverse trigonometric functions that rely on either a static or a dynamic definition of angle. Although the textbooks favor a conception of trigonometric functions that is based on a dynamic conception of angle, they split in their definition of inverse trigonometric functions. We argue that transparency in making explicit how these conceptions can be bridged might be useful in understanding difficulties that emerge when solving problems with inverse trigonometric functions.