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Trigonometric Functions


Solving trigonometric equations -using the graphs

Since the graphs are cyclic, there is always more than one x value for each y value

For example, sin30 = 0.5 only

however, sin-10.5 = 30 or 150 for values between 0 to 360

The graph is symmetrical, y is 0 at x=0 and x=180. Since 0.5 is 30 away from the origin, the next 0.5 reading must be 30 from x=180 (see the x curve above)

Solving trigonometric equations -using the CAST diagram

The letters stand for "All", "Sin", "Tan", "Cos"


Example, sin-10.5 = 30 (by calculator)

Using the diagram you can work out that the other value must be 150. If you type sin 150 into your calculator, you should get 0.5!


Whichever function you have (sin, cos or tan), reflect the value you have in any axis so that the answer appears in a quadrant in which that function is positive. If you have 'tan', you need to reflect twice


Although you need to know about the CAST diagram for your exam, most people find picturing the graphs' axes of reflection easier.


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