The Calculator supports three notations for angles: radians, degrees, and degrees-minutes-seconds. When a number is presented to a function like sin that requires an angle, the current angular mode is used to interpret the number as either radians or degrees. If an HMS form is presented to sin, it is always interpreted as degrees-minutes-seconds.
Functions that compute angles produce a number in radians, a number in degrees, or an HMS form depending on the current angular mode. If the result is a complex number and the current mode is HMS, the number is instead expressed in degrees. (Complex-number calculations would normally be done in radians mode, though. Complex numbers are converted to degrees by calculating the complex result in radians and then multiplying by 180 over @c{$\pi$} pi.)
The m r (calc-radians-mode), m d (calc-degrees-mode), and m h (calc-hms-mode) commands control the angular mode. The current angular mode is displayed on the Emacs mode line. The default angular mode is degrees.