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Mathematics > Course Model Algebra II (Traditional Pathway) > Trigonometric Functions
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Mathematics | Course : Model Algebra II (Traditional Pathway)

Domain - Trigonometric Functions

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

[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.

Resources:


  • Coordinate plane
    A plane in which a point is represented using two coordinates that determine the precise location of the point. In the Cartesian plane, two perpendicular number lines are used to determine the locations of points. In the polar coordinate plane, points are determined by their distance along a ray through that point and the origin, and the angle that ray makes with a pre- determined horizontal axis.
  • Real number
    A number from the set of numbers consisting of all rational and all irrational numbers.
  • Trigonometric function
    A function (as the sine, cosine, tangent, cotangent, secant, or cosecant) of an arc or angle most simply expressed in terms of the ratios of pairs of sides of a right-angled triangle.

Predecessor Standards:

No Predecessor Standards found.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • AI.F-IF.A.1
    Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output (range) of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
  • GEO.G-SRT.C.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.
  • AII.F-TF.A.1
    Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
  • AII.F-TF.B.5
    Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*
  • AII.F-TF.C.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.
  • PC.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.
  • PC.F-TF.A.4
    (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
  • PC.F-TF.C.9
    (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
  • 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.
  • AQR.F-TF.A.4
    (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
  • AQR.F-TF.C.9
    (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.