Of course, we could make a table of values and substitute millions of values of x and join the dots. But this is very dangerous because we don't have a sense of what is going on and our joined dots will look like unrelated spaghetti.

It is best to first sketch the graphs of the 2 parts of this function on the same graph.

a(x) = 5 sin x

b(x) = 4 cos(2x + π/3)

Now, we need to add the ordinates (y-values) of each part to obtain the composite graph. Let's take a few values.

When x = 0,

a(0) = 5 sin 0 = 0
b(0) = 4 cos(π/3) = 4

Adding these,

a(0) +b(0) = 0 + 4 = 4

Likewise, when x = 1,

a(1) = 5 sin 1 = 4. 21
b(1) = 4 cos(2 + π/3) = -3. 98

Adding gives:

a(1) + b(1) = 0.23

Similarly, for x = 2, a(2) + b(2) = 5.86

x = 3: a(3) + b(3) = 3.59

x = 4: a(4) + b(4) = -7.50

x = 5: a(5) + b(5) = -4.59

Notice that the two crests near x = 2.5 have added together to give a large crest. The two troughs near x = 4.5 have added together to give a deep trough.