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This Exploration allows you to read off the coordinates from a unit circle to find the trigonometric ratios for angles other than those found in triangles.
The applet below shows a unit circle similar to the one on page 3-15 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 30o 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.
- When P is at 30o as shown initially, use the green lines to find
(a) sin30o
(b) cos30o
(c) tan30o
- Repeat question 1 to complete the table below, so that you have a record of the ratios for each value of the central angle. (Dont forget to include the sign of the values on the axes.) Compare your answers for the acute angles with the table you produced in Techlab 3.2.
| Angle(degrees) | 30 | 45 | 60 | 120 | 150 | 210 | 240 | 330 |
| Sine | | | | | | | | |
| Cosine | | | | | | | | |
| Tangent | | | | | | | | |
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