# Common Core Standards for 8-12

Number and Quantity - Category
Algebra - Category
Geometry

Categories: Geometry SRT / Modeling ★

Geometry -Category

G-SRT Similarity, right triangles, and trigonometry

Understand similarity in terms of similarity transformations

CC_G-SRT-1 Verify experimentally the properties of dilations given by a center and a scale factor:

a.  A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
b.  The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

CC_G-SRT-2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
CC_G-SRT-3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Prove theorems involving similarity

CC_G-SRT-4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

CC_G-SRT-5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Define trigonometric ratios and solve problems involving right triangles

CC_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.
CC_G-SRT-7 Explain and use the relationship between the sine and cosine of complementary angles.
CC_G-SRT-8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

★ Apply trigonometry to general triangles

CC_G-SRT-9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
CC_G-SRT-10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.
CC_G-SRT-11 (+) 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).

Trigonometry

Categories: Functions IF and TF / Geometry SRT / Modeling ★

Functions - Category

F-IF Interpreting functions

Analyze functions using different representations

CC_F-IF-7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. ★ (modeling)
e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F-TF Trigonometric Functions

Extend the domain of trigonometric functions using the unit circle

CC_F-TF-1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
CC_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.
CC_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.
CC_F-TF-4 (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Model periodic phenomena with trigonometric functions

CC_F-TF-5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.★ (modeling)
CC_F-TF-6 (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
CC_F-TF-7 (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.★ (modeling)

Prove and apply trigonometric identities

CC_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.
CC_F-TF-9 (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Geometry -Category

G-SRT Similarity, right triangles, and trigonometry

Define trigonometric ratios and solve problems involving right triangles

CC_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.
CC_G-SRT-7 Explain and use the relationship between the sine and cosine of complementary angles.
CC_G-SRT-8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

★ Apply trigonometry to general triangles

CC_G-SRT-9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
CC_G-SRT-10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.
CC_G-SRT-11 (+) 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).

(+) All standards without a (+) symbol should be in the common mathematics curriculum for all college and career ready students. Standards with a (+) symbol may also appear in courses intended for all students.
(★) Making mathematical models is a Standard for  Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol ( ★ ).