This is a Desmos-based exploration of the graphs of the reciprocal trig functions. Students need access to Desmos to complete the exploration as written.
The ability to graph y = asin(bx), y = acos(bx), and y = atan(bx) are prerequisite skills. Phase shifts and vertical shifts are explored but the objective of the exploration is sketch and analyze graphs of y = acscbx, y = asec(bx), and y = atan(bx).
The activity is completely student-based and could be done without teacher supervision. Six follow-up functions are included for use as homework or other practice.
The document is provided in Word for your convenience.