Trigonometric Equations and The Unit Circle
The solutions of the trigonometric equation sin(x) = a, where a is a real number are explored using an applet. Both the graph of sin(x)and the unit circle are used to explore the solutions of this equation as a changes.
We concentrate on the solutions in the interval [0,2Pi) and since sin(x)is periodic, finding the other solutions is not very demanding.
Once you have gone through this tutorial, you may want to go to another tutorial to solve trigonometric equations .
1 - click on the button above "click here to start" and MAXIMIZE the window obtained.
2 - Use the scrollbar to select a value of a less than -1, how many solutions are there?
3 - Use the scrollbar to select a value of a grater than 1, how many soltions are there?
4 - Select a value of a equal to 1, how many solutions are there?
5 - Select a value of a equal to -1, how many solutions are there?
6 - Select a value of a in the open interval (-1,1), how many solutions are there? See that you can link the solutions in the unit circle and the graph of sin(x).
7 - Explore now the solutions of the equations cos(x)= a on paper
More references and pages in this website related to unit circle and trigonometric equations.