What Math Should I Teach?

I have recently finished two more Squidoo pages on Quadratic Equations and Square Roots. Both of these, as have the others lenses linked to the right, force me to face the question "What Math Should I Teach?" In my mind, the Squidoo pages and the acccompanying videos I have created are designed for a regular 8th grade/freshman Algebra 1 class. But as I have learned from teaching those classes the curriculum can vary widely from class to class, school to school and state to state.

Indiana, my home state, has created a list of standards for us to follow. The Algebra 1 standards are the governing list of concepts for me to cover in an Algebra 1 class. And I use them as such. However, even with those as a guide there are many choices to make on the depth and breadth that each topic is covered. For instance, I am currently teaching basic trigonometry concepts to a high school Geometry class. The class is what FCHS refers to as a "lab" class, which means the students background puts them in a category of needing extra help to pass Geometry. Thus I am left to ask the question of how in depth do I teach the concepts to them. The Indiana Geometry standards state:

G5.4 Define and use the trigonometric functions (sine, cosine, tangent, cotangent, cosecant, secant) in terms of angles of right triangles.

G5.5 Know and use the relationship sin2(x)+cos2(x) = 1.

With this in mind I look at the two days it has taken the students to begin to grasp just the basic 3 trigonometric functions and I wonder if I can possibly cover both of those. Especially in light of the fact that I still need to cover quadrilaterals and circles before the end of the year(under 8 weeks left). I have more to say on this, and will at a later time, but I would love to hear any opinions that other teachers have on how they decide what they are going to cover.