Resolving vectors into their components

I find students encounter difficulties in resolving vectors into the components, especially when the axis is tilted or rotated. The following are some steps which I find useful to emphasize to them:

  1. Draw the axis. Without drawing the axis, it is difficult to find the components on the axis. So always draw the axis.
  2. Draw a rectangle with a diagonal line, and follow this criteria: (a) The vector we want to resolve is the diagonal line, (b) The sides of the rectangle must coincide with the axis.
  3. Indicate the known angle.
  4. Use TOA CAH SOH to determine which trigonometric functions to use.