How to calculate the area of any triangle using two sides and an included angle.
How to graph y = tan(theta) for 0 <= theta < pi/2.
How to use a counterexample to prove a definition or conjecture incorrect.
How to solve a sine equation by factoring: 4 [sin(theta)]^2 = 2.
How to define a chord; how to describe the effect of a perpendicular bisector of a chord and the distance from the center of the circle.
How to use the fundamental theorem of calculus to compute the net change of a quantity.
How to define perimeter and calculate it for squares, rectangles, and circles.
How to prove that opposite angles in a cyclic quadrilateral are congruent; how to prove that parallel lines create congruent arcs in a circle.
How to understand the idea of slope.
Understanding the science of physics.
How to define the derivative of a function at a point x=a.
How to define an antiderivative.
How to define an inverse.
How to solve a simple sine equation: sin (theta) = 1/2.
How to define the reciprocal trigonometric functions, the reciprocal identities, and the Pythagorean identities.
How to define the tangent function for all angles.