HS.F-IF.C. Interpreting Functions: Analyze functions using different representations.

• Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.⭑ (CCSS: HS.F-IF.C.7)

  • Graph trigonometric functions, showing period, midline, and amplitude. (CCSS: HS.F-IF.C.7.e)

HS.G-SRT.C. Similarity, Right Triangles, and Trigonometry: Define trigonometric ratios and solve problems involving right triangles.

• Explain and use the relationship between the sine and cosine of complementary angles. (CCSS: HS.G-SRT.C.7)

• Use trigonometric ratios to solve right triangles in applied problems.⭑ (CCSS: HS.G-SRT.C.8)

A star symbol (⭑) represents grade level expectations and evidence outcomes that make up a mathematical modeling standards category.

HS.N-CN.B. The Complex Number System: Represent complex numbers and their operations on the complex plane.

• (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. (CCSS: HS.N-CN.B.4)

• (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (–1 + √3i)3 = 8 because (–1 + √3i) has modulus 2 and argument 120°. (CCSS: HS.N- CN.B.5)

• (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. (CCSS: HS.N-CN.B.6)

HS.F-TF.A. Trigonometric Functions: Extend the domain of trigonometric functions using the unit circle.

• (+) Use radian measure of an angle as the length of the arc on the unit circle subtended by the angle. (CCSS: HS.F-TF.A.1)

• (+) 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. (CCSS: HS.F-TF.A.2)

• (+) Use special triangles to determine geometrically the values to sine, cosine, tangent for 𝜋/3, 𝜋/4, and 𝜋/6 and use the unit circle to express the values sine, cosine, and tangent for x, 𝜋 + x, and 2𝜋 – x and in terms of their values for x where x is any real number. (CCSS: HS.F-TF.A.3)

• (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. (CCSS: HS.F-TF.A.4)

HS.F-TF.B. Trigonometric Functions: Model periodic phenomena with trigonometric functions.

• (+) Model periodic phenomena with trigonometric functions with specified amplitude, frequency, and midline.⭑ (CCSS: HS.F-TF.B.5)

• (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. (CCSS: HS.F-TF.B.6)

• (+) Use inverse function to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.⭑ (CCSS: HS.F-TF.B.7)

HS.F-TF.C. Trigonometric Functions: Prove and apply trigonometric identities.

• (+) 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. (CCSS: HS.F-TF.C.8)

• (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. (CCSS: HS.F-TF.C.9)

HS.G-SRT.D. Similarity, Right Triangles, and Trigonometry: Apply trigonometry to general triangles.

• (+) Derive the formula A = 1/2absin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. (CCSS: HS.G-SRT.D.9)

• (+) Prove the Laws of Sines and Cosines and use them to solve problems. (CCSS: HS.G-SRT.D.10)

• (+) 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). (CCSS: HS.G-SRT.D.11)

A star symbol (⭑) represents grade level expectations and evidence outcomes that make up a mathematical modeling standards category.

Please visit the complete 2020 Colorado Academic Standards for High School Mathematics to view the following:

• Colorado Essential Skills and Mathematical Practices connections

• Inquiry Questions

• Coherence Connections