How to describe the unit circle. How to draw the unit circle and label its parts. How to strategize about finding coordinates on the unit circle.
How to derive the equation for a circle using the distance formula.
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 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).