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Mathematics > Course Model Advanced Quantitative Reasoning (Advanced Course) > Trigonometric Functions
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Mathematics | Course : Model Advanced Quantitative Reasoning (Advanced Course)

Domain - Trigonometric Functions

Cluster - Extend the domain of trigonometric functions using the unit circle.

[AQR.F-TF.A.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.

Resources:


  • Cosine
    A trigonometric function that for an acute angle is the ratio between a leg adjacent to the angle when the angle is considered part of a right triangle and the hypotenuse.
  • Real number
    A number from the set of numbers consisting of all rational and all irrational numbers.
  • Sine (of an acute angle)
    The trigonometric function that for an acute angle is the ratio between the leg opposite the angle when the angle is considered part of a right triangle and the hypotenuse.
  • Tangent
    a) Meeting a curve or surface in a single point if a sufficiently small interval is considered. b) The trigonometric function that, for an acute angle, is the ratio between the leg opposite the angle and the leg adjacent to the angle when the angle is considered part of a right triangle.

Predecessor Standards:

  • 8.G.B.7
    Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • AI.F-BF.B.3
    Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Include linear, quadratic, exponential, and absolute value functions. Utilize technology to experiment with cases and illustrate an explanation of the effects on the graph.
  • GEO.G-SRT.C.7
    Explain and use the relationship between the sine and cosine of complementary angles.
  • AII.F-TF.A.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.
  • MI.F-BF.B.3
    Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Include linear and exponential models. (Focus on vertical translations for exponential functions). Utilize technology to experiment with cases and illustrate an explanation of the effects on the graph.
  • MII.G-SRT.C.7
    Explain and use the relationship between the sine and cosine of complementary angles.
  • MIII.F-TF.A.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.