Final answer:
An oscilloscope and older CRT television sets require a sawtooth waveform for their time-base and deflection circuits to control the electron beam's movement across the screen.
Step-by-step explanation:
The device that requires a sawtooth waveform is an oscilloscope in its time-base circuits or a television set in its deflection circuits. A sawtooth waveform is characterized by its linear, ramp-like ascending slope followed by an abrupt descent. This shape is crucial for applications such as controlling the movement of an electron beam in cathode-ray tubes (CRTs), which are found in older television sets and oscilloscopes. The linear ascending part of the waveform allows the beam to sweep across the screen smoothly, while the rapid descent resets the beam's position back to the starting point.