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Graphs of Trigonometric Functions: Cosecant, Tangent, and Their Characteristics

This guide explores the graphs of the cosecant (csc) and tangent (tan) functions, detailing their unique properties and characteristics. Key points include the period, amplitude, and behaviors of the functions. The cosecant graph, as the reciprocal of sine, is undefined when sine is zero and exhibits asymptotic behavior. The tangent function also has distinct features, including its periodicity and lack of defined amplitude. The guide includes examples of graphing these functions and finding asymptotes without graphing.

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Graphs of Trigonometric Functions: Cosecant, Tangent, and Their Characteristics

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  1. 4.3 Graphing Other Trig Functions

  2. Graph of y = cscx Reciprocal of sine Graph sine first cscx is und when sin x = 0 cscx = 1 when sin x = 1 cscx = 2 when sin x = ½ cscx = –1 when sin x = –1 cscx = –2 when sin x = –½ 1 –1 Amp is undefined Period = 2π You find sec x the same way!! Graph cosx first! Then take the reciprocal!

  3. Ex 1) Graph Factor out b b c a d = 2 = = = 0 Check Period: Per = IL: Check a point:

  4. Graph of y = tan x x y 1 –1 Period = π Amplitude = not defined

  5. General Tangent Curve  Diff from sin & cos!! middle point of graph  Diff from sin & cos!!

  6. Ex 2) Graph Factor out b b c a d = = = 2 = 0 Check Period: (middle) 2 –2 Per = IL: Check a point:

  7. Ex 3) Graph Factor out b Graph tan first b c a d = 2 = = = 0 Check Period: (middle) Per = IL: cot x is reciprocal of tan x Check a point:

  8. Homework #403 Pg 205 #5, 9, 17 – 19, 21 – 24 (no graph), 26 – 28, 30, 34 – 40, 43, 44 To find asymptotes without graphing set the argument equal to where the parent graph has asymptotes and solve

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