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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 - Prove and apply trigonometric identities.

[AQR.F-TF.C.9] - (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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.
  • 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:

No Predecessor Standards found.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • GEO.G-SRT.B.5
    Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
  • 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.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.
  • 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.
  • MII.G-SRT.B.5
    Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
  • MII.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.
  • 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.
  • MIII.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.N-CN.B.5
    (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example: (-1+√3i)3=8 because (-1+ √3i) has modulus 2 and argument 120°.