| (a) |
Derive the equation of a circle with centre $(0,0)$ and radius $r$. |
| (b) |
Derive the equation of the unit circle from the application of the Pythagorean theorem or the distance formula. |
| (c) |
Develop and generalize the six trigonometric ratios in terms of $x$, $y$, and $r$, using a point that is the intersection of the terminal arm of an angle with the unit circle. |
| (d) |
Develop, generalize, and apply strategies for determining the six trigonometric ratios for any angle given a point on the terminal arm of the angle. |
| (e) |
Determine, with technology, the approximate value of the trigonometric ratios for any angle (in radians or degrees). |
| (f) |
Develop, generalize, explain, and apply strategies, including using the unit circle or a reference triangle, for determining the exact trigonometric ratios for angles whose measures are multiples of $0°$, $30°$, $45°$, $60°$, $90°$ (when expressed in degrees), $ 0, π/6, π/4, π/3 $, or $ π/2 $ (when expressed in radians). |
| (g) |
Explain and apply strategies (with or without the use of technology) to determine the measures, in degrees or radians, of the angles in a specified domain that have a particular trigonometric ratio value. |
| (h) |
Explain and apply strategies to determine the exact values of the other trigonometric ratios, given the value of one trigonometric ratio in a specified domain. |
| (i) |
Sketch a diagram to represent the context of a problem that involves trigonometric ratios. |
| (j) |
Solve situational questions using trigonometric ratios. |
