An electric current, I, in amps, is given by I = cos(wt) + √5 sin(wt) where w does not equal zero is a constant. What are the maximum and minimum values of I?

Question

An electric current, I, in amps, is given by

I = cos(wt) + √5 sin(wt)

where w does not equal zero is a constant. What are the maximum and minimum values of I?

Minimum value of I:

Maximum value of I:

(I became stuck after taking the derivative and setting the function equal to zero... Thanks for the help!!)

Answer 1

A sinusoid of the form: a cos(θ) + b sin(θ) can be rewritten as

A cos( θ - φ) where A = sqrt( a² + b² ) and φ = arctan( b/a)

For this problem a = 1 and b = sqrt(5) , so A = sqrt(6)

Therefore the maximum current will be sqrt(6) and the minimum - sqrt(6)

Of course there are time values for which the current is zero.