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Section 4.6

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Section 4.6

Graphs of Other Trigonometric Functions

- In this section we examine the graphs of the other four trigonometric functions.
- After looking at the basic, untransformed graphs we will examine transformations of tangent, cotangent, secant, and cosecant.
- Again, extensive practice at drawing these graphs using graph paper is strongly recommended.

- Three key elements of tangent and cotangent:
- For which angles are tangent and cotangent equal to 0? These will be x-intercepts for your graph.
- For which angles are tangent and cotangent undefined? These will be locations for vertical asymptotes.
- For which angles are tangent and cotangent equal to 1 or -1? These will help to determine the behavior of the graph between the asymptotes.

|A| = amplitude (affects the places where tangent or cotangent is equal to 1 or -1)

π/B = period (distance between asymptotes). The asymptotes will keep their same relative position

C/B = phase (horizontal) shift. Left if (+), right if (-)

- The graphs of secant and cosecant are derived from the graphs of cosine and sine, respectively:
- Where sine and cosine are 0, cosecant and secant are undefined (location of vertical asymptotes).
- Where sine and cosine are 1, cosecant and secant are also 1.
- Where sine and cosine are -1, cosecant and secant are also -1.

- To graph a transformation of cosecant or secant, graph the transformation of sine or cosine, respectively, then use the reciprocal strategy previously discussed:

|A| = amplitude (affects the places where secant or cosecant is equal to 1 or -1)

2π/B = period (distance between asymptotes)

C/B = phase (horizontal) shift, left if (+), right if (-)