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Department: Mathematics Understanding by Design Course: Algebra 2 Standard(s): CC.9-12.G.SRT.6 Define trigonometric ratios and solve problems involving right triangles. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. CC.9-12.G.SRT.7 Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship between the sine and cosine of complementary angles. CC.9-12.G.SRT.8 Define trigonometric ratios and solve problems involving right triangles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. CC.9-12.G.SRT.9 (+) Apply trigonometry to general triangles. Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. CC.9-12.G.SRT.10 (+) Apply trigonometry to general triangles. Prove the Laws of Sines and Cosines and use them to solve problems. CC.9-12.G.SRT.11 (+) Apply trigonometry to general triangles. Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). Stage 1: Desired Results Understandings Exploring Trigonometric Functions - Chapter 14 Triangles are found in many fields and aspects of the real world, and finding missings sides and angles can be essential to these applications. There are many types of triangles, and these may need to be set up and solved for differently. Essential Questions Why does SOHCAHTOA not work for all triangles? Why is SSA called the ambiguous case? S T A G E 1 Knowledge & Skill Students can use their calculators to evaluate trigonometric functions. Students can determine whether to use SOHCAHTOA, Law of Sines, or Law of Cosines. Students can use SOHCAHTOA to solve for missing pieces of right triangles. Students can use the Law of Sines and the Law of Cosines to solve non-right triangles. Students can use trigonometry to find the area of triangles. Vocabulary: Sine (sin) Cosine (cos) Tangent (tan) Cosecant (csc) Secant (sec) Cotangent (cot) Trigonometric Identity Pythagorean Theorem Trigonometric Ratio Law of Sines Law of Cosines Stage 2: Assessment Evidence Students will demonstrate their understanding through daily classwork, daily homework, quizzes, and a unit test. The teacher will also use questioning to verify understanding during the day's lesson. The teacher can use warm-up problems, board work, math bingo (and other games), and other activities related to this unit during the instruction. S T A G E 2 Performance Task Summary Quizzes Unit Test Rubric Titles Course groups will meet to determine point values for tests. Self-Assessments Other Evidence, Summarized Daily Classwork Daily Homework Stage 3: Learning Activities S T A G E 3 Lecture Notes Mind Maps/Graphic Organizers (dependent on teacher) Board work/math games Daily classwork (example problems) Daily Homework Reviews Quizzes Unit Test