Express 10sin(ƒÖ.t+ƒÎ�€4) in the form AsinƒÖ.t + BcosƒÖ.t
To express 10sin(ωt+φ) in the form Asin(ωt) + Bcos(ωt), we can use the trigonometric identity sin(A+B) = sinAcosB + cosAsinB.
Let's apply this identity to our expression:
10sin(ωt + φ) = 10(sin(ωt)cos(φ) + cos(ωt)sin(φ))
By comparing with Asin(ωt) + Bcos(ωt), we can identify A and B as follows:
A = 10cos(φ)
B = 10sin(φ)
Therefore, 10sin(ωt + φ) can be expressed as Asin(ωt) + Bcos(ωt) by substituting the values of A and B we found:
10sin(ωt + φ) = 10cos(φ)sin(ωt) + 10sin(φ)cos(ωt)
So, to express 10sin(ωt + φ) in the form Asin(ωt) + Bcos(ωt), we can use the trigonometric identity sin(A+B) = sinAcosB + cosAsinB and substitute the values of A and B.