Express 10sin(ƒÖ.t+ƒÎ�€4) in the form AsinƒÖ.t + BcosƒÖ.t
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Certainly! I apologize for the confusion. Let's retype the expression using commonly-used symbols:
Express 10sin(ωt+φ/4) in the form Asin(ωt) + Bcos(ωt).
To express the given expression in the desired form, we need to make use of the trigonometric identity sin(α + β) = sinαcosβ + cosαsinβ.
Given: 10sin(ωt + φ/4)
Using the trigonometric identity sin(α + β) = sinαcosβ + cosαsinβ, we can rewrite the expression as:
10sin(ωt)cos(φ/4) + 10cos(ωt)sin(φ/4)
Now, let's simplify further using the following trigonometric identities:
sin(φ/4) = √2/2
cos(φ/4) = √2/2
Now, we can rewrite the expression as:
(10/2)sin(ωt) + (10/2)cos(ωt)
Finally, we can express it in the desired form:
Asin(ωt) + Bcos(ωt)
Where:
A = 10/2 = 5
B = 10/2 = 5
So, 10sin(ωt + φ/4) can be expressed as 5sin(ωt) + 5cos(ωt).