UNIT 2 ALGEBRA II TEMPLATE CREATED BY REGION 1 ESA UNIT 2

Transcription

1 UNIT 2 ALGEBRA II TEMPLATE CREATED BY REGION 1 ESA UNIT 2

2 Algebra II Unit 2 Overview: Trigonometric Functions Building on their previous work with functions, and on their work with trigonometric ratios and circles in Geometry, students now use the coordinate plane to extend trigonometry to model periodic phenomena. e: It is important to note that the units (or critical areas) are intended to convey coherent groupings of content. The clusters and standards within units are ordered as they are in the Common Core State s, and are not intended to convey an instructional order. Considerations regarding constraints, extensions, and connections are found in the instructional notes. The instructional notes are a critical attribute of the courses and should not be overlooked. For example, one will see that standards such as A.CED.1 and A.CED.2 are repeated in multiple courses, yet their emphases change from one course to the next. These changes are seen only in the instructional notes, making the notes an indispensable component of the pathways. (All instructional notes/suggestions will be found in italics throughout this document) Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol Template created by Region 1 ESA Page 2 of 8

3 Unit 2: Trigonometric Functions- F.TF.1 Cluster: Extend the domain of trigonometric functions using the unit circle. Instructional es: none F.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. I can define unit, circle, central angle, and intercepted arc. I can define the radian measure of an angle. I can extend the definition of radian measure to show that an angle measure of one radian occurs when the length of the arc and the radius of the circle are the same. I can use a similarity approach to find the radian measure of central angles in circles that are not unit circles. #1 Make sense of problems and persevere in solving them. When does a function best model a Assessments align to suggested learning targets. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning #4 Model with mathematics Drill and practice #5 Use appropriate tools strategically. Multiple choice #6 Attend to precision. Short answer (written) Performance (verbal explanation) #7 Look for and make use of structure Product / Project #8 Look for and express regularity in repeated reasoning. Radian, central angle, intercepted arc, length, unit circle Template created by Region 1 ESA Page 3 of 8

4 Unit 2: Trigonometric Functions- F.TF.2 Cluster: Extend the domain of trigonometric functions using the unit circle. Instructional es: none F.TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. I can define a radian and unit circle. I can label the unit circle in radians since it is known that one revolution of the unit circle is equal to 2 radians. I can draw central angles of given radian measures on the unit circle with the vertex at the origin and the initial ray on the positive x-axis. I can recall that in the unit circle, the cosine of an angle is defined to be the x- coordinate where the terminal ray of angle crosses the unit circle. #1 Make sense of problems and persevere in solving them. When does a function best model a Assessments align to suggested learning targets. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning #4 Model with mathematics Drill and practice #5 Use appropriate tools strategically. Multiple choice #6 Attend to precision. Short answer (written) Performance (verbal explanation) #7 Look for and make use of structure Product / Project #8 Look for and express regularity in repeated reasoning. Radian, unit circle, co-terminal angle, output, evaluate, trigonometric function Template created by Region 1 ESA Page 4 of 8

5 Unit 2: Trigonometric Functions- F.TF.2 continued Cluster: Extend the domain of trigonometric functions using the unit circle. Instructional es: none F.TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. I can recall that on the unit circle, the sine of an angle is defined to be the y-coordinate where the terminal ray of angle crosses the unit circle. I can identify the cosine and sine of an angle when given a graph of the unit circle with the coordinates labeled. I can explain why the right triangle definitions of cosine and sine do not allow cosines and sines to have negative values. I can explain why the unit circle definitions of cosine and sine allow cosine and sines to have negative values. #1 Make sense of problems and persevere in solving them. When does a function best model a Assessments align to suggested learning targets. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning #4 Model with mathematics Drill and practice #5 Use appropriate tools strategically. Multiple choice #6 Attend to precision. Short answer (written) Performance (verbal explanation) #7 Look for and make use of structure Product / Project #8 Look for and express regularity in repeated reasoning. Radian, unit circle, co-terminal angle, output, evaluate, trigonometric function Template created by Region 1 ESA Page 5 of 8

6 Unit 2: Trigonometric Functions- F.TF.2 continued Cluster: Extend the domain of trigonometric functions using the unit circle. Instructional es: none F.TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. I can define co-terminal angles. I can identify many co-terminal angles when given a radian measure. I can explain why co-terminal angles will all produce the same output when evaluated as the inputs of a trigonometric function. #1 Make sense of problems and persevere in solving them. When does a function best model a Assessments align to suggested learning targets. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning #4 Model with mathematics Drill and practice #5 Use appropriate tools strategically. Multiple choice #6 Attend to precision. Short answer (written) Performance (verbal explanation) #7 Look for and make use of structure Product / Project #8 Look for and express regularity in repeated reasoning. Radian, unit circle, co-terminal angle, output, evaluate, trigonometric function Template created by Region 1 ESA Page 6 of 8

7 Unit 2: Trigonometric Functions- F.TF.5 Cluster: Model periodic phenomena with trigonometric functions. Instructional es: none F.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. I can define amplitude, frequency, and midline of a trigonometric function. I can explain the connection between frequency and period. I can recognize real-world situations that can be modeled with a periodic function by identifying the amplitude, frequency (or period), and midline. I can write a function notation for the trigonometric function that models a problem situation, given the amplitude, frequency (or period), and midline of a periodic situation. #1 Make sense of problems and persevere in solving them. When does a function best model a Assessments align to suggested learning targets. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning #4 Model with mathematics Drill and practice #5 Use appropriate tools strategically. Multiple choice #6 Attend to precision. Short answer (written) Performance (verbal explanation) #7 Look for and make use of structure Product / Project #8 Look for and express regularity in repeated reasoning. Amplitude, frequency, midline, trigonometric function, periodic function Template created by Region 1 ESA Page 7 of 8

8 Unit 2: Trigonometric Functions- F.TF.8 Cluster: Prove and apply trigonometric identities. Instructional es: An Algebra II course with an additional focus on trigonometry could include the (+) standard F.TF.9: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. This could be limited to acute angles in Algebra II. F.TF.8 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin (θ), cos (θ), or tan (θ), given sin (θ), cos (θ), or tan (θ), and the quadrant of the angle. I can derive the Pythagorean identity sin 2 (Ѳ) + cos 2 (Ѳ) = 1 by using the unit circle definitions of cosine and sine and applying the Pythagorean Theorem. I can use the Pythagorean identity sin 2 (Ѳ) + cos 2 (Ѳ) = 1 to calculate the value of sin(ѳ) or cos (Ѳ) when I am given sin (Ѳ) or cos (Ѳ) and the quadrant of Ѳ. I can use the quotient identity (tan (Ѳ) = sin Ѳ / cos Ѳ ) to calculate tan (Ѳ). #1 Make sense of problems and persevere in solving them. When does a function best model a Assessments align to suggested learning targets. #2 Reason abstractly and quantitatively. #3 Construct viable arguments and critique the reasoning #4 Model with mathematics Drill and practice #5 Use appropriate tools strategically. Multiple choice #6 Attend to precision. Short answer (written) Performance (verbal explanation) #7 Look for and make use of structure Product / Project #8 Look for and express regularity in repeated reasoning. Pythagorean identity Pythagorean Theorem, unit circle, sine, cosine, tangent, quotient identity Template created by Region 1 ESA Page 8 of 8