Techlab 3.7

The applet below shows a unit circle similar to the one on page 3-18 of your text.
Instructions
Click the button "Lab 3.4". The red dot represents point "P" on the wheel so that the line joining the dot and the hub (centre) of the wheel makes an angle of 30^o with the horizontal. If you press the key "P" on the keyboard of your computer, the point P will rotate counter-clockwise in the positive direction. Pressing "N" will make P move clockwise in the negative direction. The green line on both axes represents the x and y coordinates of the angle that forms P. Answer the questions below.

1. (a) When P is at 30^o, use the green lines to write the coordinates for P as accurately as you can, to two decimal places. Use the unit circle definition and these coordinates to find:
   i. sin30^o
   ii. cos30^o
   iii. tan30^o
   (b) Verify your answers (taking into account measurement accuracy) using a calculator.

2. (a) Write the coordinates for Q(150^o) as accurately as you can, to two decimal places. Use the unit circle definition and these coordinates to find:
   i. sin 150^o
   ii. cos 150^o
   iii. tan 150^o
   (b) Verify your answers (taking into account measurement accuracy) using a calculator.

3. (a) Write the coordinates for R(210^o) as accurately as you can, to two decimal places. Use the unit circle definition and these coordinates to find:
   i. sin 210^o
   ii. cos 210^o
   iii. tan 210^o
   (b) Verify your answers (taking into account measurement accuracy) using a calculator.

4. (a) Write the coordinates for S(330^o) as accurately as you can, to two decimal places. Use the unit circle definition and these coordinates to find:
   i. sin 330^o
   ii. cos 330^o
   iii. tan 330^o
   (b) Verify your answers (taking into account measurement accuracy) using a calculator.

5. Write a paragraph describing all the patterns and similarities you notice from this investigation. Can you make any conjectures?