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Unit Circle: Intro & Review DATE: 1/24 CLASS PERIOD: PreCalc UNIT: U.C.-1 LESSON OBJECTIVES: Students will review vocabulary related to Trig and the Unit Circle, rules for radicals in the denominator, and trig ratios (Soh-Cah-Toa). Students will also derive side lengths of special right triangles in HW. This lesson corresponds with Common Core State Standards-Geometry-SRTDefine trigonometric ratios and solve problems involving right triangles (6-8). MATERIALS Pre-test; note cards for card sort; notes for differentiated learners. EVALUATION Results of Card Sort; observations during work time. Worksheet collected the next day. REVIEW Vocab; rationalization; soh-cah-toa HOMEWORK ASSIGNMENTS Worksheet 1-1. ACTIVITIES TO EXTEND UNDERSTANDING AND/OR RELATED TOPICS Last few problems on worksheet are Special Right Triangles. Schedule Pre-test (10’) Opening (10’) Review (5’) Soh-Cah-Toa (7’) Work Time (13’) Activities Give pre-test as required by GTEP. Card Sort with vocab from Trig & U.C. Take time to go over each term. Reminders on rationalization and leaving answers in precise (non-decimal) terms. Review Soh-Cah-Toa and work some simple ratio examples. Worksheet with radical problems, soh-cah-toa problems, and special right triangles. . Name _____________________ Unit Circle 1-1 Worksheet 1. Rationalize the following fractions. a. 2 b. √3 2 √2 c. 17 d. √5 2 √4 2. Find sin, cos, and tan. Leave answers in reduced fraction form. α sin α = cos α = tan α = 13 5 sin β = cos β = tan β = β 12 3. Find 𝑥 in the following triangles. a. b. 30 45 𝑥 2 𝑥 1 60 1 45 1 c. d. 45 30 𝑥 𝑥 1 1 60 45 𝑥 .5 Unit Circle Lesson 1-1 Notes Vocabulary & Review Definitions Angle. Given two lines that intersect, the amount of rotation around the point of intersection required for one line to meet the other. Arc. A portion of the circumference of a circle. Circle. The set of points in plane that are the same distance from a given point. Circumference. The perimeter of a circle. Hypotenuse. The longest side in a right triangle; the side opposite the right angle. Radius. The distance from the center of a circle to its perimeter. Rationalization of Fractions In most branches of math, it is considered improper to leave a square root on the bottom of a fraction. So we must practice what is called “rationalizing” the fraction to keep whole numbers in the denominator. Write some examples from the board in the space below, but here is one to get you started. 1 √2 √2 ∗ = 2 √2 √2 A Note on Non-Decimal Answers In Trigonometry (which is the topic of this unit), answers often have or a square root in them. Instead of using calculators to get decimal approximations, just leave your answers in this form: .707…). 𝜋 2 (instead of 1.57…) or √2 2 (instead of Soh-Cah-Toa (a Review of Trig Ratios) 𝑠𝑖𝑛𝑒 = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 , 𝑐𝑜𝑠𝑖𝑛𝑒 = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 , 𝑡𝑎𝑛𝑔𝑒𝑛𝑡 = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 (draw a diagram on the back that shows opposite, adjacent, and hypotenuse)