Arkansas flagArkansas: T Math Standards

14 standards · 2 domains

T.3

  • T.3.PC.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
  • T.3.PC.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 around the unit circle.
  • T.3.PC.3 (+) Use special right triangles to determine geometrically the exact values of sine, cosine, tangent for π/3, π/4, π/6, and π/2. (+) 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 exact values for x where x is any real number.
  • T.3.PC.4 (+) Develop the Pythagorean identity, sin^2(θ) + cos^2(θ) = 1. (+) Given sin(θ) , cos(θ), or tan(θ) and the quadrant of the angle, use the Pythagorean identity to find the remaining trigonometric functions.
  • T.3.PC.5 (+) Develop the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
  • T.3.PC.6 Derive the formula A = (½)ab sin C for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
  • T.3.PC.7 Prove the Law of Sines and the Law of Cosines and use them to solve problems.
  • T.3.PC.8 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.
  • T.3.PC.9 Define and use reciprocal functions, cosecant, secant, and cotangent to solve problems.

T.4

  • T.4.PC.1 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions
  • T.4.PC.2 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
  • T.4.PC.3 (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
  • T.4.PC.4 (+) Use inverse functions to: Solve trigonometric equations that arise in modeling context(s); Evaluate the solutions of trigonometric equations, with or without technology, and Interpret the solutions of trigonometric equations in terms of the context(s).
  • T.4.PC.5 Recognize that some trigonometric equations have infinitely many solutions and be able to state a general formula to represent the infinite solutions