Determining secant/cosecant equations for a graph

[Random-Hero-]

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?

 

[tiny-tim]

Hi Random-Hero-!

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

 

[Random-Hero-]

would it be these?

secant: -3sec(4x)

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

 

[tiny-tim]

would it be these?

secant: -3sec(4x)

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

I think you're just guessing …

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

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

(and what is the period?)

 

[Random-Hero-]

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?

 

[tiny-tim]

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?