I'm answering the following question:

```
Find the maximum and minimum values for the function f(x) = 2 / (1 + 3cos(θ) + 4sin(θ))

```

I have found that the answer shows that the **minimum** occurs at the point (53.1 degrees, 1/3) and the **maximum** occurs at (233.1 degrees, -0.5). 

This doesn't really intuitively make much sense to me. How is it possible that the minimum occurs above the maximum on the graph? I understand that the aforementioned function has no *absolute* maximum or minimum, but doesn't it make sense that locally the minimum would be lower than the maximum point?

I am working through a book and that is the answer given. 

To get to such, 3cos(θ) + 4sin(θ) is put into harmonic form, giving 5sin(t+36.9). 

From 2 / (1 + 5sin(θ+36.9)), the knowledge that f(x) will obtain a maximum when sin(θ+36.9) = 1 and a minimum when sin(t+36.9) = -1 is used to get to the answer by solving for (θ+36.9) = arcsin(1) and (θ+36.9)=arcsin(-1), respectively. However, it puts the local maximum below the local minimum.