If g(x.y) = cos(3x + 4y) , what is the range of g(x,y) in interval notation?

Question

 I know that the range of cos(x) is [-1,1], but I'm not sure how to calculate the range for this function.

Answer 1

Since both x and y can be any real numbers, 3x + 4y can generate arguments for the cosine over all of [0,2π].  Hence, the output of the cosine function should cover the full range of [-1,1].  

 

You know that

 

-1 ≤ cos(3x + 4y) ≤ 1

 

x = π/3 and y = 0 gives -1.  

x = 0 and y = 0 gives 1.

 

You can see that you span the entire range of [-1,1].