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Common Core: Math
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 Student Outcomes Students define the tangent function and understand the historic reason for its name. Students use special triangles to determine geometrically the values of the tangent function for...

 Student Outcomes Students define the secant function and the cofunctions in terms of points on the unit circle. They relate these names for these functions to the geometric relationships among lines...

 Student Outcomes Students graph the sine and cosine functions and analyze the shape of these curves. For the sine and cosine functions, students sketch graphs showing key features, which include...

 Student Outcomes Students explore horizontal scalings of the graph of y =sin(x). Students convert between degrees and radians.

 Student Outcomes Students observe identities from graphs of sine and cosine basic trigonometric identities and relate those identities to periodicity, even and odd properties, intercepts, end...

 Students will use trigonometric functions to model periodic phenomena (FTF.B.5) by fitting sinusoidal functions to data (SID.B.6a). Students use the properties of the graphs of sinusoidal...

 Student Outcomes Students formalize the periodicity, frequency, phase shift, midline, and amplitude of a general sinusoidal function by understanding how the parameters A, w, h, and k in the formula...

 Student Outcomes Students review how changing the parameters A, ω, h, and k in f(x) = A sin(ω(x  h)) + k affects the graph of the sine function. Students examine the example of the Ferris wheel,...

 Student Outcomes Students graph the tangent function. Students use the unit circle to express the values of the tangent function for π  x, π + x, and 2π  x in terms of tan(x), where x is any real...

 Student Outcomes Students prove the Pythagorean identity sin2(x) + cos2(x) = 1. Students extend trigonometric identities to the real line, with attention to domain and range. Students use the...

 Student Outcomes Students prove simple identities involving the sine function, cosine function, and secant function. Students recognize features of proofs of identities.

 Student Outcomes Students see derivations and proofs of the addition and subtraction formulas for sine and cosine. Students prove some simple trigonometric identities.

 In this topic, students develop an understanding of the six basic trigonometric functions as functions of the amount of rotation of a point on the unit circle (FTF.A.1), and then translate that...

 Student Outcomes Students prove the Pythagorean identity sin2(x) + cos2(x) = 1. Students extend trigonometric identities to the real line, with attention to domain and range. Students use the...

 Student Outcomes Students prove simple identities involving the sine function, cosine function, and secant function. Students recognize features of proofs of identities.

 Student Outcomes Students see derivations and proofs of the addition and subtraction formulas for sine and cosine. Students prove some simple trigonometric identities.

 Exponential and Logarithmic Functions In this module, students synthesize and generalize what they have learned about a variety of function families. They extend the domain of exponential functions...

 In Topic A, students both review what they already know about exponential expressions and functions with integer exponents, and extend the meaning of an exponential expression to allow for first...

 At the beginning of Topic B, students apply the properties of exponents to solve exponential equations numerically (FBF.1a) as a way to motivate the need for logarithms, which are first introduced...

 Student Outcomes Students approximate the value of quantities that involve positive irrational exponents. Students extend the domain of the function f(x) =bx for positive real numbers b to all real...

 Student Outcomes Students write an exponential function that represents the amount of water in a tank after t seconds if the height of the water doubles every 10 seconds. Students discover Euler’s...

 Student Outcomes Students solve simple exponential equations numerically.

 Student Outcomes Students calculate a simple logarithm using the definition.

 Student Outcomes Students construct a table of logarithms base 10 and observe patterns that indicate properties of logarithms.