Download Unit 14

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?
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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.
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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
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Lecture Notes
Mind Maps/Graphic Organizers (dependent on teacher)
Board work/math games
Daily classwork (example problems)
Daily Homework
Reviews
Quizzes
Unit Test