

Unit 2 Algebra II 


Unit Topic and
Length: Building on their previous work with functions, and on their work with trigonometric ratios and circles in Geometry, in Unit 2 students will now use the coordinate plane to extend trigonometry to model periodic phenomena. In Geometry students will have used basic trigonometric ratios to solve problems involving right triangles. This unit will be the first introduction to the concept of a radian as an angle measure. Students will understand the radian measure of an angle as the length of the arc on the unit circle subtended by the angle. Students will understand the unit circle and its usefulness to extend trigonometric functions to all real numbers. Additionally, students will prove the Pythagorean identity sin^{2}(θ) + cos^{2}(θ) = 1, and use it in their work with angles, measures, and location. Work in this unit will prepare students for more extensive graphing, interpreting, and modeling of trigonometric functions, along with other functions, in Unit 3. 

Standards for Mathematical
Practice 

MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of
others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. 



*A radian measure of an angle is the length
of the arc on the unit circle subtended by the angle. *The unit circle enables the extension of the domain of
trigonometric functions to include all real numbers. *Trigonometric functions can be used to model periodic phenomena. *The Pythagorean identity 
Essential Questions: *How can you find the measure of an angle in radians? *What is the unit circle? *How can you use the unit circle to define the trigonometric
functions of an angle? *What are the characteristics of the reallife problems that can be
modeled by trigonometric functions? *How can you verify a trigonometric identity? 


