On how to prove the equation, the first part of the problem

Asin(wt + φ) = c2sinwt +c1coswt

Step-by-step explanation:

Proof:

wt here is periodic where as φ is constant

taking left hand side

Asin(wt + φ)

Using trigonometric identity sin(θ+φ) = sinθcosφ +sinφcosθ

Asin(wt +φ) = A[sinwtcosφ +sinφcoswt]

                  = Asinwtcosφ +Asinφcoswt

Now as we know φ is constant

so will Asinφ and Acosφ will also be constant

let     Asinφ= c1

and Acosφ=c2

Putting in above expression, we get

Asin(wt +φ) = c2sinwt +c1coswt !

the range is 19

step-by-step explanation:

the range is biggest number minus the smallest, so in this case it would be

41 - 22 = 19

answer: it is 1: 47 pm