1. All students understand the notion of angle, and how to measure it, both in degrees and radians. They can convert between degrees and radians.

2. All students know the definition of sine and cosine as y and x coordinates of points on the unit circle, and are familiar with the graphs of the sine and cosine functions.

3. All students know the identity cos2(x) + sin2(x) = 1

• All students prove that this identity is equivalent to the Pythagorean theorem (i.e., all students can prove this identity using the Pythagorean theorem, and conversely they can prove the Pythagorean theorem as a consequence of this identity)
  
• All students prove other trigonometric identities, and simplify others using the identity cos2(x) + sin2(x) = 1 (e.g., all students use this identity to prove that sec2(x) = tan2(x) + 1).
  

4. All students graph functions of the form f(t) = Asin (Bt + f) or f(t) = Acos (Bt + f), and interpret A, B, and f in terms of amplitude, frequency, period, and phase shift.

5. All students know the definition of the tangent and cotangent functions, and can graph them.

6. All students know the definitions of the secant and cosecant functions, and can graph them.

7. All students know that the tangent of the angle a line makes with the x-axis is equal to the slope of the line.

8. All students know the definitions of the inverse trigonometric functions, and can graph the functions.

9. All students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points.

10. All students demonstrate understanding of the addition formulas for sines and cosines, their proofs, and use them to prove and/or simplify other trigonometric identities.

11. All students demonstrate understanding of half angle and double angle formulas for sines and cosines, and can use them to prove and/or simplify other trigonometric identities.

12. All students use trigonometry to determine unknown sides or angles in right triangles.

13. All students know the Laws of Sines and the Law of Cosines, and apply them to problems.

14. All students determine the area of a triangle given one angle and the two adjacent sides.

15. All students are familiar with polar coordinates. In particular, they can determine polar coordinates of a point given in rectangular coordinates, and vice versa.

16. All students represent equations given in rectangular coordinates in terms of polar coordinates.

17. All students are familiar with complex numbers. They can represent a complex number in polar form, and know how to multiply complex numbers in their polar form.

18. All students know De Moivre's Theorem, and can give n-th roots of a complex number given in polar form.

19. All students are adept at using trigonometry in a variety of applications and word problems.