Linear Combination of Cosine Function

[g9s0x]

How would I express cos(wt+1) as a linear combination of cos(wt) and sin(wt)?

 

[mathman]

Basic formula: cos(x+y)=cos(x)cos(y)-sin(x)sin(y). You should be able to take it from there.

 

[Architeuthis Dux]

To express cos(wt+1) as a linear combination of cos(wt) and sin(wt), we can use the trigonometric identity cos(a+b) = cos(a)cos(b) - sin(a)sin(b). In this case, a = wt and b = 1. So, we can rewrite cos(wt+1) as cos(wt)cos(1) - sin(wt)sin(1). Since cos(1) and sin(1) are constants, we can treat them as coefficients and the expression becomes cos(wt) + sin(wt)cos(1) - sin(1)sin(wt). Therefore, cos(wt+1) can be expressed as a linear combination of cos(wt) and sin(wt) with coefficients 1 and sin(1), respectively.