9-12 Common Core Standards
In the CCGPS Analytic Geometry course, students were introduced to right triangle trigonometry and its applications. In this unit, students will expand their understanding of trigonometry as they are asked to use the unit circle to define the trigonometric functions. They will come to understand angle measurement in both degrees and radians. Students are also provided with experiences in applying the six trigonometric functions as functions of angles in standard position and as functions of arc lengths on the unit circle. At the conclusion of this unit study, students should be able to find values of trigonometric functions by using the unit circle.
The following standards are addressed throughout this unit:
MCC9-12.G.SRT.6 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.
MCC9-12.G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
MCC9-12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
MCC9-12.F.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
MCC9-12.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.
MCC9-12.F.TF.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number.
MCC9-12.F.BF.4 Find inverse functions.
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning
References
The Common Core State Standard Initiative. (2011). Common core state standards
for mathematics. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
The following standards are addressed throughout this unit:
MCC9-12.G.SRT.6 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.
MCC9-12.G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
MCC9-12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
MCC9-12.F.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
MCC9-12.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.
MCC9-12.F.TF.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number.
MCC9-12.F.BF.4 Find inverse functions.
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning
References
The Common Core State Standard Initiative. (2011). Common core state standards
for mathematics. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf