Verified answer

First, I learned you had to derive that first

so if you derive the function, it is

g'(x) = 4-sec^2(x) right?

and we had to make that equal to 0 so

0 = 4-sec^2(x)

now solve for x

sec^2(x) = 4

square root both side and you get

sec(x) = +- 2

and we know sec(x) = 1/cos(x)

so 1/cos(x) = +- 2

From here, make it in fraction form

1/cos(x) = 2/1 and cross multiply

1 = 2cos(x)

now divide both sides by 2 and you get

1/2 = cos(x)

for what angle (x) will cos(x) equal 1/2?, angles are 60 and 300

do the same thing I did above but this time with -2

1 = -2cos(x)

-1/2 = cos(x)

Angles(x) for cos(x) to equal -1/2 are 120 and 240

now we have angles 60, 120, 240 and 300 for the x value.

We know from pre-calc that Pi = 3.14 or angle-wise, 180 degrees

Now we know the pi and the radian form and that 60 = pi / 3

if you do this on your calculator, pi/3 = 3.14/3 which should be 1.047 which is what you got for your lowest value

120 = 2pi/3 = 2.094

240 = 4pi/3 = 4.189 (what you got)

300 = 5pi/3 = 5.236

So answers are 1.047, 2.904, 4.189, 5.236 in this order.

I think what you didn't do is when you square rooted sec^2(x) = 4

you didn't think of -2 and did only sec(x) = 2

that's how you got angle 60, and 240, but not 120 and 300 which are -1/2 value for cos(x)

Hope this helped.