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Exploring the Concepts of Trigonometric Functions and Their Graphs

This warm-up activity engages students in evaluating trigonometric functions, specifically tangent and cotangent at various key angles. Students will analyze fundamental properties of secant, cosecant, tangent, and cotangent and their relationships to sine and cosine graphs. They will graph multiple functions, including sine, cosecant, secant, tangent, and cotangent, while identifying where tangent and cotangent are undefined. The activity emphasizes understanding periods of functions and their graphical representations.

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Exploring the Concepts of Trigonometric Functions and Their Graphs

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  1. Warm Up Jan. 26th • Evaluate the following: a. tan(0) b. tan(π/4) c. tan(π/2) d. tan(3π/4) e. tan(π) f. cot(0) g. cot(π/4) h. cot(π/2) i. cot(3π/4) j. cot(π) • Write an equation for the graph below.

  2. Homework Questions??

  3. Graphing Secant, Cosecant Tangent & Cotangent

  4. Remember… How are the graphs of cos and sec related? How are the graphs of sin and csc related?

  5. Graph: y = 2sin(4x)

  6. Graph: y = 2csc(4x)

  7. Graph: y = 1 – 4sec(x – π/6)

  8. Graphing tangent… Where is tangent undefined??? What is the period of y = tan x?

  9. Graph: y = 2tan(3x)

  10. Graph: y = - ½tan(x + π/4)

  11. Graphing co-tangent… Where is cot undefined??? How is the graph of y = cot x related to the graph of y = tan x?

  12. Graph: y = 2cot(4x)

  13. Graph: y = - cot(2x + π/4)

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