Students discover trigonometry, which allows them to synthesize knowledge of transformations and properties of other functions while offering a new perspective on functions through periodicity.
High school math sequences typically include trigonometric functions as the final example of functions in the curriculum. Trigonometry offers an opportunity to synthesize knowledge of transformations and properties of other functions while offering a new perspective on functions through periodicity.
Trigonometry supports calculus, as the trigonometric functions have fascinating relationships through differentiation and integration and offer a great opportunity to practice calculus skills involving rate of change and accumulation.
While trigonometry is necessary for calculus, it also offers avenues to explore for their own sake. Students must connect geometric interpretations of sine and cosine, the unit circle, and the sine and cosine function and look at these three different mathematical structures as examples of the same underlying idea. Trigonometry also offers an opportunity to model periodic contexts in the world and to better understand phenomena around us.
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Sine | Cosine | Tangent | Unit circle |
Midline | Amplitude | Period | Periodic function |
Degrees/Radians | Special Right Triangles | Secant | Cosecant |
Cotangent | Standard position | Initial ray | Terminal ray |
Sinusoidal curve | Odd/Even functions | Symmetrical |
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Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
Unit-Specific Intellectual Prep
This assessment accompanies Unit 6 and should be given on the suggested assessment day or after completing the unit.
F.IF.C.7.E
F.TF.A.4
F.TF.B.5
Sketch sine graphs to model contextual situations and identify features of sine graphs.
F.IF.C.7.E
F.TF.B.5
Sketch cosine graphs to model contextual situations and identify features of cosine graphs.
F.TF.A.2
F.TF.A.4
Find values of specific points on the unit circle using geometry.
F.TF.A.2
F.TF.A.4
Evaluate sines and cosines of points at reference angles on the unit circle.
F.TF.A.2
F.TF.A.3
Describe the relationship between the unit circle and tangent.
F.TF.A.2
F.TF.A.3
Define and evaluate the trigonometric functions of tangent, cosecant, secant, and cotangent.
F.TF.A.1
F.TF.A.3
Convert between degrees and radians and evaluate trigonometric functions written in radians.
F.TF.A.1
F.TF.A.3
Evaluate transformations of sine, cosine, and tangent such as $${2{\pi-x}}$$, $${\pi-x}$$, and $${\pi+x}$$.
F.IF.C.7.E
F.TF.A.1
F.TF.A.3
F.TF.A.4
Graph transformations of sine and cosine functions (Part I).
F.IF.C.7.E
F.BF.B.3
Graph transformations of sine and cosine functions (Part II).
F.IF.C.7.E
F.BF.B.3
Graph transformations of tangent functions.
F.BF.B.3
F.TF.A.3
F.TF.B.5
Identify equations and graphs of all six trigonometric functions.
F.TF.A.3
F.TF.B.5
Model contextual situations using trigonometric functions (Part I).
F.TF.A.3
F.TF.B.5
Model contextual situations using trigonometric functions (Part II).
Key: Major Cluster Supporting Cluster Additional Cluster
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