Calculus with Constants

Question

An electric current, I, in amps, is given by I=cos(wt)+√(8)sin(wt), where w≠0 is a constant. What are the maximum and minimum values of I?

I have tried finding the derivative, but after that, I do not know how to solve for 0 because of the constant w.

Answer 1

Well David,you can convert this function into one trigonometric function by multiplying and dividing it by

√(1^2 + 8) i.e, 3. So your function becomes like this

I = 3*(1/3 cos(wt) + √8/3 sin(wt))
  = 3* sin(wt + atan(1/√8))

Now, you can easily say its maximum value is I = 3 amp and minimum value is I = 0 amp.