u=0.4sin(a)+cos(a). What is a when u reaches it maximum value.?

Question

I tried some approaches,but my answer doesn't seem to be correct.
btw,my answer is 68.2 and proved to be wrong

Answer 1

As a previous responder wrote, take the derivative and set it to zero. But, the next step is much simpler:
0.4 cos a - sin a =0
0.4 = tan a
a=0.3805 radians or 21.8°

If you don't know calculus, do it with a graphing calculator.

Answer 2

Take the first derivative and set it to 0:

0.4cos a-sin a = 0

To solve this, use (sin a)^2 = 1 - (cos a)^2
So:
0.4cos a = sina
Square:
0.16cos^2a = sin^2a
0.16cos^2a = 1-cos^2a

1.16cos^2a = 1
cos a = positive or negitive square root of 1/1.16

a is then computed as the arccos.

Answer 3

Should be arctan(.4) = .3805063771 radians = 21.8degrees
du/da = .4cos(a) -sin(a)
Set this = 0 getting :
.4cos(a)-sin(a) = 0
.4 cos(a) = sin(a)
.4 = sin(a)/cos(a) = tan(a)
a = arctan(.4)