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F - Trigonometric Functions

This text resource illustrates the Standards Map for the Functions Overview Trigonometric Functions domain in the Common Core State Standards.

Standards

  2. Common Core Mathematics: Functions > TF

    Trigonometric Functions (TF)

  3. Common Core Mathematics: Functions > TF > C.1

    Extend the domain of trigonometric functions using the unit circle

  4. Common Core Mathematics: Functions > TF > C.1 > S.1

    Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

    Content Skills Learning Targets Big Ideas Essential Questions
    2 - Understand (angle's radian measure is the arc length of the intercepted angle)
    2 - I can understand that an angle's radian measure is the arc length of the intercepted angle on the unit circle.
    A. Angles can be measured in degrees and radians.
    A.1 What is a radian?
  5. Common Core Mathematics: Functions > TF > C.1 > S.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.

    Content Skills Learning Targets Big Ideas Essential Questions
    2 - Explain (unit circle on coordinate plane extends trigonometric functions to real numbers)
    2 - Interpret (trig functions in terms of radian measure of angles)
    2 - I can explain how the unit circle on coordinate plane extends trigonometric functions to real numbers.
    2 - I can interpret trig functions in terms of radian measure of angles.
    A. Trig functions can be extended to real numbers.
    A.1 How do trig functions connect to other functions?
  6. Common Core Mathematics: Functions > TF > C.1 > S.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, cosines, and tangent for x, π+x, and 2π–x in terms of their values for x, where x is any real number.

    Content Skills Learning Targets Big Ideas Essential Questions
    3 - Use (special triangles to find sine, cosine, and tangent for n/3)
    3 - Use (special triangles to find sine, cosine, and tangent for n/4)
    3 - Use (special triangles to find sine, cosine, and tangent for n/6)
    3 - Use (unit circle to find sine, cosine, and tangent for x in terms of x)
    3 - Use (unit circle to find sine, cosine, and tangent for n+x in terms of x)
    3 - Use (unit circle to find sine, cosine, and tangent for 2n-x in terms of x)
    3 - I can use special triangles to find sine, cosine, and tangent for n/3.
    3 - I can use special triangles to find sine, cosine, and tangent for n/4.
    3 - I can use special triangles to find sine, cosine, and tangent for n/6.
    3 - I can use the unit circle to find sine, cosine, and tangent for x in terms of x.
    3 - I can use the unit circle to find sine, cosine, and tangent for n+x in terms of x.
    3 - I can use the unit circle to find sine, cosine, and tangent for 2n-x in terms of x.
    A. One can use special triangles or the unit circle to find values for trig functions of specific angles.
    A.1 Do I have to use the unit circle to find values of trig functions?
  7. Common Core Mathematics: Functions > TF > C.1 > S.4

    (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

    Content Skills Learning Targets Big Ideas Essential Questions
    3 - Use (unit circle to explain odd and even symmetry)
    1 - 3 Use (unit circle to explain periodicity of trig functions)
    3 - I can use the unit circle to explain odd and even symmetry.
    1 - 3 I can use the unit circle to explain periodicity of trig functions.
    A. Trigonometric functions have periodicity.
    A.1 What is periodicity?
  8. Common Core Mathematics: Functions > TF > C.2

    Model periodic phenomena with trigonometric functions

  9. Common Core Mathematics: Functions > TF > C.2 > S.5

    Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

    Content Skills Learning Targets Big Ideas Essential Questions
    Trigonometric functions
    4 - Model (trig functions using specific amplitude, period, frequency, and midline)
    4 - I can model trig functions using specific amplitude, period, frequency, and midline.
    A. Trigonometric functions can undergo transformations just as other functions do.
    A.1. What is the amplitude of a trig function?
    A.2. How do I find the frequency of a trig function?
    A.3. How do I find the midline of a trig function?
  10. Common Core Mathematics: Functions > TF > C.2 > S.6

    (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

    Content Skills Learning Targets Big Ideas Essential Questions
    Trigonometric functions
    2 - Understand (restricting domain allows construction of inverse)
    2 - I can understand restricting domain allows construction of inverse.
    A. Trigonometric inverses are used in problem solving.
    A.1 How can I use trigonometric inverses?
  11. Common Core Mathematics: Functions > TF > C.2 > S.7

    (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

    Content Skills Learning Targets Big Ideas Essential Questions
    3 - Use (inverse functions to solve trig equations)
    2 - Evaluate (solutions using technology)
    2 - Interpret (solutions in terms of context)
    3 - I can use inverse functions to solve trig equations.
    2 - I can evaluate solutions using technology.
    2 - I can interpret solutions in terms of the context.
    A. Inverse trigonometric functions are used when solving trig equations.
    A.1 What is an inverse trig function and how is it used?
  12. Common Core Mathematics: Functions > TF > C.3

    Prove and apply trigonometric identities

  13. Common Core Mathematics: Functions > TF > C.3 > S.8

    Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to calculate trigonometric ratios.

    Content Skills Learning Targets Big Ideas Essential Questions
    sin^2(B) + cos^2(B) = 1
    3 - Prove (sin^2[B]+cos^2[B]=1)
    3 - Use (sin^2[B]+cos^2[B]=1)
    3 - I can prove the Pythagorean identity sin^2[B]+ cos^2[B] = 1.
    3 - I can use sin^2[B] + cos^2[B] = 1 to calculate trig ratios.
    A. Trigonometric identities are useful in calculation.
    A.1 How can I use a trig identity?
  14. Common Core Mathematics: Functions > TF > C.3 > S.9

    (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

    Content Skills Learning Targets Big Ideas Essential Questions
    for sine, cosine, tangent
    3 - Prove (addition formulas for sine, cosine, tangent)
    3 - Prove (subtraction formulas for sine, cosine, tangent)
    3 - Use (addition formulas for sine, cosine, tangent to solve problems)
    3 - Use (subtraction formulas for sine, cosine, tangent to solve problems)
    3 - I can prove addition formulas for sine, cosine, tangent.
    3 - I can prove subtraction formulas for sine, cosine, tangent.
    3 - I can use addition formulas for sine, cosine, tangent to solve problems.
    3 - I can use subtraction formulas for sine, cosine, tangent to solve problems.
    A. Identities can be useful tools in problem solving.
    A.1 How can I use the addition and subtraction identities?

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