How to use the distance formula to derive the equation for a circle.
How to write the parametric equations of a circle centered at (0,0) with radius r, oriented counter-clockwise.
How to express a vector algebraically in terms of the unit vectors i and j.
How to use the unit circle to derive the tangent identity and the Pythagorean identity.
How to use the unit circle to derive identities that are useful in graphing the reciprocal trigonometric functions.
How to graph y = tan(theta) for 0 <= theta < pi/2.
How we define sine and cosine for all angle measures using the unit circle.
How to define the tangent function for all angles.
How to define the reciprocal trigonometric functions, the reciprocal identities, and the Pythagorean identities.
How to graph the special cases of the family r = a + b cos (theta) when a or b = 0.
How do we measure sine and cosine of pi/4?
How to solve a sine equation by factoring: 4 [sin(theta)]^2 = 2.
How to derive the cosine of a difference formula.
How to measure the sine and cosine of 150.
How to evaluate expressions like tan(sin (4/5))^(-1).
How to compute the cross product of two 3D vectors.
How to create the different conic sections.
How to identify a conic section by its formula.
How to convert a polar equation into rectangular form.