What is angle modulation and its types?

Hint: When attempting questions like the one given to us above, the first thing to do is to brush up our concepts regarding amplitude, frequency and other terms regarding waves. Keep in mind the various concepts surrounding frequency or phase of carrier signals to message signals.

Complete answer:
Sinusoidal or sine wave is basically a wave which depicts a recurring change or motion. It is known as sine wave because it has a similar shape as the sine function, when it is plotted on a graph, which shows the repetition of one wave segment in a repeated manner.
Cosine wave is similar to a cosine function when depicted on a graph, hence the name of cosine wave. Both sine and cosine waves are similar in appearance but they are not the same, because every cosine function is a shifted sine function. In simple terms cosine function is moved to the left by an amount of\[\dfrac{\pi }{2}\].
Angle modulation is basically a method to modulate a sinusoidal carrier in which either frequency or phase of the carrier varies according to the message signal, but at the same time keeping the carrier amplitude constant.
Angle modulation has many advantages and a few disadvantages as well, like it helps in noise reduction, improved system fidelity and helps in more efficient usage of power. At the same time it has some disadvantages like increased bandwidth and the requirement of using more complex circuits.
Angle modulation can basically be largely classified into two types; Frequency modulation and phase modulation.
Frequency modulation or FM is basically where frequency of the carrier is varied according to the message signal. It is widely used for FM broadcasting or radio programming.
Phase modulation or PM is basically where the phase angle of the carrier varies according to the message signal. It is used widely in cellular and satellite telecommunications, and even in digital subscriber line systems and Wi-Fi.

Note: Modulating signals in frequency and phase modulation can be analogous in nature or it may be digital but in general when using digital signals to modify carrier waves, keying is used as the preferred method. Thus telecommunication modems use frequency-shift keying, phase shift keying et cetera.