Your grammar book certainly has several pages on this topic.
As Jonathan mentioned, you will hear many acceptable versions.
My cousin is arriving at 5:30 PM. ("standard textbook answer," common)
My cousin arrives at 5:30 PM. (common)
My cousin is going to arrive at 5:30 PM. (common)
My cousin will arrive at 5:30 PM. (common)
My cousin will be arriving at 5:30 PM. (common)
Briefly, the simple present (We "verb") and present continous (We are "verb"-ing) are used for scheduled future events (events that are viewed as certain to occur). The simple present usually applies to transportation and the present continuous usually applies to people. Examples: "My plane leaves at 0920 on January 3, 2019." (transportation) "My wife and I are leaving for France on January 3, 2019 and we are returning on January 17." (people) My wife and I have tickets, so it is viewed as a certain future event.
The near future (We are going to "verb") is used for planned future events (events that are viewed as certain, highly probable, or probable). Examples: "After supper, I am going to read a book." "My wife and I are going to leave for France in January." The near future continuous (We are going to be "verb"-ing) is also possible.
Also, the near future can be used for predictions about the near future. Example: "The clouds are dark. It is going to rain soon."
The simple future (We will <verb>) is used for intended future events (events which are viewed as general intentions without a plan). Examples: "My wife and I will visit France next year." The near future continuous (We will be "verb"-ing) is also possible.
There are additional uses of the simple future such as to make a decision or to make a promise.
Importanlty, the simple future can be used as a generic future tense. In this usage, it is never "wrong."
The excellent grammar book "Grammar in Use Intermediate" by Murphy has five units on these topics.