Sine and Cosine Finder

sine and cosine finder

Sines and cosines pop on your calculator screen like magic. Here is a visual way to understand what these trigonometric ratios mean in a unit circle. A ruler slides back and forth in the horizontal slot. You can read the sine and cosine of the angle on the ruler.


  1. Cut out the pattern pieces.
  2. Cut out the horizontal slot out of the larger piece to form a slot that the ruler will slide in.
  3. Cut along the thick lines on the vertical ruler.
  4. Fold the tabs on the ruler. Dashed lines are valley folds and dot-dashed lines are mountain folds.
  5. Slip the tabs of the ruler into the slot on the larger piece.
  6. Line up the ruler so the left edge touches the circle at the angle you are interested in.
  7. Determine the sine of the angle by reading the value on the vertical ruler.
  8. Determine the cosine of the angle by reading the value on the horizontal ruler.