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 This module revisits trigonometry that was introduced in Geometry and Algebra II, uniting and further expanding the ideas of right triangle trigonometry and the unit circle. New tools are introduced...

 Module 2 builds on students’ previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of...

 Student Outcomes Students determine the values of the sine, cosine, and tangent functions for rotations of π/3, π/4, and π/6 radians. Students use the unit circle to express the values of the sine,...

 Topic A helps students recall how to use special triangles positioned within the unit circle to determine geometrically the values of sine, cosine, and tangent at special angles. The unit circle is...

 Student Outcomes Given the probability distribution of a discrete random variable in table or graphical form, students describe the longrun behavior of the random variable. Given a discrete...

 Student Outcomes Students graph the sine, cosine, and tangent functions and analyze characteristics of their graphs.

 Student Outcomes Students understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. Students use...

 Student Outcomes Students use inverse trigonometric functions to solve realworld problems addressing best viewing angles.

 Student Outcomes Students model situations using trigonometric functions and will apply inverse trigonometric functions to solve problems in modeling contexts.

 In this topic, students extend their understanding of probability, building on work from Grade 11. The multiplication rule for independent events introduced in Grade 11 is generalized to a rule that...

 Student Outcomes Students use the general multiplication rule to calculate the probability of the intersection of two events. Students interpret probabilities in context.

 Student Outcomes Students use the fundamental counting principle to determine the number of different possible outcomes for a chance experiment consisting of a sequence of steps. Students calculate...

 Student Outcomes Students calculate the number of different combinations of items selected from a set of distinct items.

 Student Outcomes Students distinguish between situations involving combinations and situations involving permutations. Students use permutations and combinations to calculate probabilities. Students...

 Student Outcomes Students distinguish between discrete random variables and continuous random variables. Given the probability distribution for a discrete random variable in table or graphical form,...

 The graphs of the trigonometric functions are revisited in Topic C. Students visualize these graphs with the aid of the appropriate software and briefly recall how changing various parameters of a...

 Student Outcomes Students prove the subtraction formula for cosine and use their understanding of the properties of the trigonometric functions to derive the remaining addition and subtraction...

 Student Outcomes Students use the addition formulas to derive the doubleangle formulas for sine, cosine, and tangent and evaluate trigonometric expressions for specific values of θ. Students use the...

 Student Outcomes Students model waveforms using sinusoidal functions and understand how standing waves relate to the sounds generated by musical instruments. Students use trigonometric identities to...

 Student Outcomes Students explore the symmetry and periodicity of trigonometric functions. Students derive relationships between trigonometric functions using their understanding of the unit circle.

 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 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,...