Find the Maximum value and the Minimum value of y for (1 Viewer)

[Utility]

y = sin(x) - cos(x)

x is between 0 and 2pi.

 

[Carrotsticks]

3 methods of doing this.

1. Converting that expression into a single trigonometric expression using Auxiliary Angles, then finding the max/min of that. This is the easiest in my opinion because by simple inspection, we see that the Amplitude is going to be root 2.

2. Sketching y=sin(x) and y=-cos(x) and adding the two curves, but this is difficult because you wouldn't really have an exact answer due to human error.

3. Actually differentiating it and letting it be equal to 0 etc, and solving for x. Upon doing so, sub back into the equation and observe that the Y value is plus/minus root 2.

 

[Utility]

Thanks. I did the third option & it didn't match the set answers... so I thought I did something wrong. After looking at it again, they've got y and x in the wrong order... (x = + / - root 2 <-- incorrect in the text).