Vector space of the function sin(x + ø) |
| 06.05.2014, 19:20 | happyrobot | Auf diesen Beitrag antworten » |
| Vector space of the function sin(x + ø) Show that the set of functions V = { f(x) = Asin(x + ø)|A ∈ ℝ, ø ∈ [0,2]} generates a vector space over the field of real numbers. Find a basis for V and determine its dimension. Hint: The addition theorems for trigonometric functions are helpful for the solution, in particular sin(x+y) = sin(x)cos(y) + sin(y)cos(x). |
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| 06.05.2014, 20:29 | happyrobot | Auf diesen Beitrag antworten » |
| RE: Vector space of the function sin(x + ø) Can someone please give me some tips and help me out ---> Show that the set of functions V = { f(x) = Asin(x + ø)|A belongs to Real numbers, ø belongs to [0,2 Pai]} generates a vector space over the field of real numbers. Find a basis for V and determine its dimension. Hint: The addition theorems for trigonometric functions are helpful for the solution, in particular sin(x+y) = sin(x)cos(y) + sin(y)cos(x). |
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