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Aedan Gonzales 2022-05-07 Answered
The equation is
a cos ( ω t ) + b sin ( ω t ) = A cos ( ω t + ϕ )
I must have forgotten how the right hand side follows from the left hand side.
Some hints would be helpful
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Answers (2)

Taniya Wood
Answered 2022-05-08 Author has 19 answers
Let A = a 2 + b 2 and ϕ be an angle such that cos ϕ = a a 2 + b 2 and sin ϕ = b a 2 + b 2
Then, by using the identity cos ( x + y ) = cos x cos y sin x sin y, we have:
a cos ( ω t ) + b sin ( ω t ) = a 2 + b 2 [ a a 2 + b 2 cos ( ω t ) b a 2 + b 2 sin ( ω t ) ] = A [ cos ϕ cos ( ω t ) sin ϕ sin ( ω t ) ] = A cos ( ω t + ϕ ) .
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Hailee Stout
Answered 2022-05-09 Author has 7 answers
Try breaking down A cos ( ω t + ϕ )
A cos ( ω t + ϕ ) = A ( cos ω t cos ϕ sin ω t sin ϕ ) = ( A cos ϕ ) cos ω t ( A sin ϕ ) sin ω t
Try to show that for arbitrary constants a and b that there exists constants A and ϕ such that
a = A cos ϕ
and
b = A sin ϕ
What is a 2 + b 2 ?
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