Lesson plan
|Teacher: Cathy Hobensack |School Year: 2014-2015 |
|Course: Applied Trigonometry |Intended Grade Level: 12th |
| |
|Course Summary This course will begin with a review of right triangle concepts and radical properties before moving to the trigonometric functions and angles in |
|standard position. We will study the trig functions, beginning with SOHCAHTOA, the graphs of each of the trigonometric functions, the Unit Circle, and oblique |
|triangles. Analytical trigonometry, which involves trig identities and equations will follow and we will end with applications of trigonometry, vectors, complex |
|numbers, and polar coordinates and equations. |
|Course Outcomes: |
|By the end of the course, students will know: the three basic trigonometric functions of the sine, cosine, and tangent, algebraically and graphically, and how to |
|use them in triangles to find altitudes, magnitudes, directions, distances and angles measures. |
| |
|By the end of the course, students will be able to: (1) see the relevance of trigonometry in everyday life and (2) apply the above knowledge of periodic |
|trigonometric functions to natural phenomena such as astronomy, navigation, architecture, tides, monthly temperatures, heartbeats, and/or electrical currents… |
| |
|Standards Targeted[1] |
|Common Core State Standards |
|NCTM Standards |
|Units of Study |
|Units Topic |Primary Learning Outcome |
|Introduction to Trigonometric Functions |Review and use geometric terms and concepts as they relate to trigonometry, |
| |investigate similar triangles and their properties, find function values of any |
| |angle, and apply trigonometric functions to find missing lengths and angles |
|Acute Angles and Right Triangles |Find trigonometric function values of acute angles and non-acute angles, use the |
| |calculator to find trigonometric function values, solve right triangles, solve |
| |applied trigonometric problems involving angles of elevation and depression, and |
| |bearings |
|Radian Measure and Circular Functions |Use and apply radian measure, find function values of any angle in radian |
| |measure, evaluate circular functions using the unit circle, find angular and |
| |linear speeds |
|Graphs of Sinusoidal Functions, and other Trigonometric Functions |Graph periodic functions sine and cosine, identify and graph translations of the|
| |sine and cosine graphs, graph the tangent, use trigonometric functions and graphs|
| |to interpret phenomena that are periodic |
|Trigonometric Identities |Use fundamental identities, verify trigonometric identities, use and apply |
| |difference identities for cosine, sine, and tangent, use double-angle identities,|
| |and use half-angle identities |
|Inverse Circular Functions and Trigonometric Equations |Use and find function values of inverse circular functions for the sine, cosine, |
| |tangent, solve trigonometric equations using fundamental identities, double and |
| |half angle identities, and inverse identities |
|Applications of Trigonometry and Vectors |Solve oblique triangles using the law of sines, solve oblique triangles using the|
| |law of cosines, use operations of vectors, and apply vectors |
|Complex Numbers and Polar Equations |Review complex numbers and their operations, write the trigonometric form of |
| |complex numbers, use the product and quotient theorems in trigonometric form, use|
| |De Moivre’s Theorem, and graph and solve polar equations |
| | |
|Advanced Learner Recommendations |
|Advanced learners in Applied Trigonometry should consider taking Academic Trigonometry. Advanced learners can see the teacher for a higher level/more motivating |
|application to real world problems. These students can focus on the conceptual thinking by doing less practice problems and more concept check and application |
|problems. |
|Struggling Learner Recommendations |
|Flex period is available to struggling learners to get help with homework or review material covered in class. Struggling students can get extra practice and |
|tutorial online help, , which is directly correlated with this course and textbook. Struggling students enroll in Applied Trigonometry will |
|concentrate on the three basic trigonometric functions of the sine, cosine, and tangent. Testing offers multiple choice, matching, true/false problems along with |
|the regular completion problems. |
| |
|IEP Students: All accommodations included in student’s Individual Educational Plan will be followed and modifications to the regular trigonometry curriculum will |
|be made as needed for extra practice, testing, and homework by the learning support teacher. |
-----------------------
[1] Indicate primary Standards emphasis:
- PA Core - Math / ELA / Science & Technology / History & Social Studies
- National Content Standards (Name and Type)
- Industry Recognized Standards (Name and Type)
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