When solving trigonometric equations, we find all the angles
that make the equation true. If there is no interval given, use
periodicity to show the infinite number of solutions. Two ways
to visualize the solutions are (1) the graph in the coordinate
plane and (2) the unit circle. The unit circle is the more
useful of the two in obtaining an answer. I want to talk about
trigonometric equations. Let's start with a really simple
example, sine of theta equals a half. Remember when you're
solving equations, you're trying to find the values of the
variable that make the equation true so we want to find all the
angles for which the sine is one half. Now I've drawn the
picture a graph of y equals sine theta and I want to show you
that I've also drawn a graph of y equals one half and so you can
see that there are infinitely many points where sine of theta
does actually equal half. It will have infinitely many points
and there are going to be two points per period so expect
infinitely many answers and expect to have t