[C, ME, PS, R, T, V]
| (a) |
Provide examples relevant to one’s self, family, or community that illustrate the need to define a standard position for angles. |
| (b) |
Sketch an angle in standard position given the measure of the angle. |
| (c) |
Determine and justify, with or without sketching, the quadrant in which an angle in standard position terminates. |
| (d) |
Determine the reference angle for an angle in standard position. |
| (e) |
Analyze, describe, and generalize the relationship between the reference angles for angles (in standard positions) that are reflections of each other across both the $x-$ and $y-$ axes (e.g., $30°$ and $150°$, or $-60°$ and $60°$). |
| (f) |
Sketch an angle in standard position given a point $P(x,y)$ on the terminal arm of the angle. |
| (g) |
Develop, generalize, explain, and apply strategies for determining a point on the terminal arm of the angle in each quadrant that has the same reference angle as the angle with $P(x,y)$ on its terminal arm. |
| (h) |
Develop, explain, and apply strategies for determining the distance between the origin and a point $P(x,y)$ on the terminal arm of an angle. |
| (i) |
Develop, generalize, explain, and apply strategies for determining the value of $sinθ$, $cosθ$, and $tanθ$ when given a point $P(x,y)$ on the terminal arm of $θ$. |
| (j) |
Develop, generalize, explain, and apply strategies for determining $sinθ$, $cosθ$, and $tanθ$ for quadrantal angles. |
| (k) |
Develop, generalize, explain, and apply strategies for determining the sign (without calculation or the use of technology) of $sinθ$, $cosθ$, or $tanθ$ for a given value of $θ$. |
| (l) |
Develop, explain, and apply strategies for solving, for all values of $θ$, equations of the form $sinθ = a$ or $cosθ =a$, where $-1 ≤ a ≤ 1$, and equations of the form $tanθ = a$, where $a$ is a real number. |
| (m) |
Analyze $30°- 60°- 90° \and 45°- 45°- 90°$ triangles to generalize about the relationship between pairs of sides in such triangles in relation to the angles. |
| (b) |
Develop, generalize, explain, and apply strategies for determining the exact value of the sine, cosine, or tangent (without the use of technology) of an angle with a reference angle of $30°, 45°, \or 60°$. |
| (b) |
Describe and generalize the relationships and patterns in and among the values of the sine, cosine, and tangent ratios for angles from $0° \to 360°$. |
| (b) |
Create and solve a situational question relevant to one’s self, family, or community which involves a trigonometric ratio. |
| (c) |
Identify angles for which the tangent ratio does not exist and explain why. |
