The [deg] and [rad] keys set the angle mode for the trig functions. The current mode is displayed in the field at the upper right of the keyboard. The default mode is radians.
The [inv] key works with [sin], [cos], and [tan]; this is indicated by the lighter background. Pressing the [inv] key and then a trig function will calculate the inverse function value (e.g. arctan).
When you click in [inv], the inverse flag is set and "I" appears in a small indicator rectangle beneath the Deg-Rad indicator. Clicking on the "I" will reset the inverse flag if it was activated by mistake.