Determining secant/cosecant equations for a graph

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Homework Help Overview

The discussion revolves around determining the equations for secant and cosecant functions based on a provided graph. Participants are exploring the relationships between these trigonometric functions and their graphical representations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to derive the equations for secant and cosecant based on visual observations of a graph. There are questions about the period of the functions and the relationship between the secant and cosecant equations. Some participants suggest drawing inverse graphs to aid in understanding.

Discussion Status

The discussion is ongoing, with various attempts to propose equations for the secant and cosecant functions. Some participants express confusion and seek clarification on the concepts involved, while others encourage providing reasoning behind the proposed equations. There is no explicit consensus on the correct equations yet.

Contextual Notes

Some participants mention feeling lost and express a desire for additional resources on reciprocal trigonometric functions. There is an emphasis on understanding the graphical relationships rather than relying solely on calculator outputs.

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Homework Statement



http://img18.imageshack.us/img18/2097/56413287.jpg [/URL]

The Attempt at a Solution



I believe that the Secant curve has the equation y = 3 Sec ( x - pi/4) However I'm having difficulty figuring out what the cosecant equation would be. Wouldn't it just be the same thing but with a csc instead of sec?
 
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Hi Random-Hero-! :smile:
Random-Hero- said:
I believe that the Secant curve has the equation y = 3 Sec ( x - pi/4)

Nooo (except for the 3) …

what is the period?

Hint: draw the inverse graph first … that should help you with both parts of the question :wink:
 
would it be these?

secant: -3sec(4x)

cosecant: -3csc(4x+pi/2)
 
Random-Hero- said:
would it be these?

secant: -3sec(4x)

cosecant: -3csc(4x+pi/2)

I think you're just guessing :rolleyes:

try again, and this time give your reasons for your answer :smile:

(remember, sec = 1/cos, and csc = 1/sin)

(and what is the period?)
 
I'm just totally lost, I genuinely have NO idea what I'm doing, I just punched those into my Ti-83 and the graph that came up looked identical, but I want to figure it out by eye. Is there a site that covers this somewhere with reciprocal trig?
 
Random-Hero- said:
I'm just totally lost …

ok, try this …

draw the inverse of the graph …

you have a graph of y against x

in pencil, draw 3/y against x (it'll be in the middle, and it should be a continuous wave) …

can you write that pencil graph as a cos or sin? :smile:
 

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