What is the minimum value of the function y = 3sin + 4cosx?

What is the minimum value of the function y = 3sin + 4cosx?

y=3sinx+4cosx=√(3^2+4^2)sin(x+θ)=5sin(x+θ)
Where Tan θ = 4 / 3
So the minimum is - 5

Find the minimum value of the following functions and the set of independent variables X when obtaining the minimum value
（1）y=-2sinx
（2）y=2-cos（x/3）

Because SiNx ∈ [- 1,1], so - 2sinx ∈ [- 2,2], so the minimum value of y = - 2sinx is - 2
Then x = π / 2 + 2K π K ∈ Z
Similarly, cos (x / 3) ∈ [- 1,1] so 2-cos (x / 3) ∈ [1,3] so the minimum value of y = 2-cos (x / 3) is 1
In this case, X / 3 = 2K π, that is, x = 2K π / 3K ∈ Z
The value of X given by the one upstairs is too narrow to consider the domain R. all the values should be stated

Function y = - 1 / 2 + 5 (1) find the value of independent variable x (2) when x takes what value, y has the minimum value, what is the minimum value
I can't make it

There is something missing in the title
Is the function expression missing the independent variable x?
If there is no mistake, the question is meaningless
Because the function y is a constant, it has nothing to do with X!

Find the function y = 3sin (2x + pie), the value of X ∈ R is the minimum, the set of independent variables X
Another problem is that there is such a sentence in the textbook:
The minimum value of sine function is - 1 if and only if x = - Pie / 2 + 2K pie, K ∈ Z
Can I regard x = - faction / 2 + 2K faction as x = 3 faction / 2 + 2K faction?
Thank you for your answer

y=3sin(2x+pi)>=-3
sin(2x+pi)=-1
2X + pi = - pi / 2 + 2kpi, K is an integer
x=-3pi/4+kpi
sure