Note that the messages arcSin and arcCos produce an object of type Radian and not of type Float.

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Note that the messages arcSin and arcCos produce an object...

Note that the messages $\operatorname{arcSin}$ and $\operatorname{arcCos}$ produce an object of type Radian and not of type Float. Furthermore, only objects of type Radian respond to $\sin$ and $\cos$. An alternative would have been to eliminate the class Radian and to permit all objects of class Float to respond to the messages $\sin$ and $\cos$. Discuss the advantages and disadvantages of these two different arrangements.

Key Concepts

Flexibility versus Clarity

Allowing generic numeric types to handle trigonometric functions increases flexibility by broadening the application of these functions; however, it can sacrifice semantic clarity. The trade-off is between the convenience of a unified type that can perform more operations and the clarity and safety that comes from using a purpose-built class to model an angle.

Method Dispatching and Overhead

Using a separate class for angles ensures that method calls, like sin and cos, are only applicable where they make sense. Although this introduces an extra layer of abstraction which might incur a slight performance or design overhead, it helps in avoiding incorrect use and maintains conceptual consistency throughout the codebase.

Type Safety

Distinguishing between specific types (like Radian versus a generic number type) enforces the correct usage of methods. In a type-safe design, only objects representing angles would have trigonometric operations, reducing the potential for misusing numeric values and catching errors at compile or runtime.

Encapsulation and Domain Modeling

Creating a dedicated type for radians encapsulates the operations and behaviors that are specific to angles. This domain modeling leads to clearer, more maintainable code by ensuring that only objects with the appropriate semantic meaning are operated on by specific methods such as sin and cos.

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