15.3. Fourier Cosine and Sine Transforms

Try these first

1. 1.

   What is the formula for the Fourier Cosine Transform?

   Hint

   Remember it's an integral using cosine.

2. 2.

   Which type of functions does the Fourier Sine Transform cater to?

   Hint

   Think about the property of sine functions.

3. 3.

   What is the primary function type for the Fourier Cosine Transform?

   • Even functions
   • Odd functions
   • Constant functions

   Hint

   Recall the cosine properties.

4. 4.

   True or False: The Fourier Sine Transform can be inverted using sine.

   • True
   • False

   Hint

   Think about the nature of inverse transformations.

5. 5.

   Given f(x) = e^(-x) on [0, ∞), find its Fourier Cosine Transform.

   Hint

   Look for integration techniques.

6. 6.

   Evaluate the Fourier Sine Transform of f(x) = x on [0, ∞). What is the significance of its form?

   Hint

   Think about integration results and function properties.