Topic: Trigonometry |
Mathematics |
| Standard 5. Understands and applies basic and advanced properties of the concepts of geometry |
| | Level IV (Grade 9-12) |
| | | Benchmark 7. | Understands the basic concepts of right triangle trigonometry (e.g., basic trigonometric ratios such as sine, cosine, and tangent) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of right triangle trigonometry |
| | | Benchmark 8. | Uses trigonometric ratio methods to solve mathematical and real-world problems (e.g., determination of the angle of depression between two markers on a contour map with different elevations) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of tangent ratio |
| | | | | 2. | Understands the concept of cosine ratio |
| | | | | 3. | Understands the concept of sine ratio |
| | | | | 4. | Determines whether a problem can be solved by using tangent ratios |
| | | | | 5. | Determines whether a problem can be solved by using cosine ratios |
| | | | | 6. | Determines whether a problem can be solved by using sine ratios |
| | | | | 7. | Uses trigonometric ratios to solve problems of angle of depression on a contour map |
| | | | | 8. | Understands the concept of angle of depression |
| Standard 8. Understands and applies basic and advanced properties of functions and algebra |
| | Level IV (Grade 9-12) |
| | | Benchmark 3. | Understands characteristics and uses of basic trigonometric functions (e.g., the sine and cosine functions as models of periodic real-world phenomena) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of a cosine function |
| | | | | 2. | Understands the concept of a sine function |
| | | | | 3. | Understands the concept of a tangent function |
| | | | | 4. | Understands that a sine function can model periodic phenomena |
| | | | | 5. | Understands that a cosine function can model periodic phenomena |
| | Level V (Grade (College Readiness)) |
| | | Benchmark 7. | Understands periodicity in the trigonometric functions and their graphs |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the periodic nature of trigonometric functions |
| | | | | 2. | Understands the periodic nature of trigonometric graphs |
| | | Benchmark 8. | Understands unit circle trigonometry |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the concept of the unit circle |
| | | | | 2. | Understands how trigonometric functions are defined on the unit circle |
| | | Benchmark 9. | Understands the Law of Sines, Law of Cosines, and basic trigonometric identities (e.g., double angle formulas, sum and difference identities) |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the Law of Sines |
| | | | | 2. | Understands the Law of Cosines |
| | | | | 3. | Understands the double angle formulas |
| | | | | 4. | Understands the trigonometric sum identities |
| | | | | 5. | Understands the trigonometric difference identities |
| | | Benchmark 10. | Understands the graph of a function of the form f(t)=Asin(Bt+C)+D or g(t)=Acos(Bt+C)+D, in terms of amplitude, frequency, period, and vertical shift, and phase shift |
| | | | Knowledge/skill statements |
| | | | | 1. | Understands the graph of the function of the form f(t) = A sin(Bt + C) + D in terms of amplitude |
| | | | | 2. | Understands the graph of the function of the form f(t) = A sin(Bt + C) + D in terms of frequency |
| | | | | 3. | Understands the graph of the function of the form f(t) = A sin(Bt + C) + D in terms of period |
| | | | | 4. | Understands the graph of the function of the form f(t) = A sin(Bt + C) + D in terms of vertical shift |
| | | | | 5. | Understands the graph of the function of the form f(t) = A sin(Bt + C) + D in terms of phase shift |
| | | | | 6. | Understands the graph of the function of the form f(t) = A cos(Bt + C) + D in terms of amplitude |
| | | | | 7. | Understands the graph of the function of the form f(t) = A cos(Bt + C) + D in terms of frequency |
| | | | | 8. | Understands the graph of the function of the form f(t) = A cos(Bt + C) + D in terms of period |
| | | | | 9. | Understands the graph of the function of the form f(t) = A cos(Bt + C) + D in terms of vertical shift |
| | | | | 10. | Understands the graph of the function of the form f(t) = A cos(Bt + C) + D in terms of phase shift |