High School Math Guide

UTAH CORE STATE STANDARDS for MATHEMATICS

Introduce f(x) = e x as a model for continuous growth (Standard F.LE.5). „ „ Standard F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quanitity increasing linearly, quadratically, or (more generally) as a polynomial function. „ „ Standard F.LE.4 For exponential models, express as a logarithm the solution to ab ct = d where a, c , and d are numbers and the base b is 2, 10, or e ; evaluate the logarithm using technology. Include the relationship between properties of logarithms and properties of exponents, such as the connection between the properties of exponents and the basic logarithm property that log xy = log x + log y . „ „ Standard F.LE.5 Interpret the parameters in a linear, quadratic, or exponential function in terms of a context. Strand: FUNCTIONS—Trigonometric Functions (F.TF) Extend the domain of trigonometric functions using the unit circle (Standards F.TF.1–3). Model periodic phenomena with trigonometric functions (Standards F.TF.5–7). „ „ Standard F.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. „ „ Standard 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. „ „ Standard F.TF.3 Use special triangles to determine geometrically the values of sine, co sine, tangent for ∏ /3, ∏ /4 and ∏ 6, and use the unit circle to express the values of sine, cosine, and tangent for ∏ – x, ∏ + x, and 2 ∏ – x in terms of their values for x, where x is any real number. „ „ Standard F.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.  „ „ Standard F.TF.7 Use inverse functions to solve trignometric equations that arise in mod eling context; evaluate the solutions using technology and interpret them in terms of context. Limit solutions to a given interval.  Strand: GEOMETRY—Similarity, Right Triangles, and Trigonometry (G.SRT) Apply trigonometry to general triangles. With respect to the general case of the Laws of Sines and Cosines, the definitions of sine and cosine must be extended to obtuse angles (Standards G.SRT.9–11). „ „ Standard 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. „ „ Standard G.SRT.10 Prove the Laws of Sines and Cosines and use them to solve problems.

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