Desperate Trig help

1. Dec 25, 2011

nando94

I have these practice trig problems for a test. I understand the simple graphs but its these more complicated ones.

y=2sec(3x-pi)

my approach:

I first find the period and phase shift. Since the period of a normal secant function which is 2pi. Then the period of this one is 2pi/3. The phase shift is pi/3. There is gonna a be a vertical strech of 2.

After that I am stuck because I dont know how to exactly graph this even though I have all the information. Its mostly because of the odd period, 2pi/3. Really confused.

2. Dec 25, 2011

SammyS

Staff Emeritus
I don't know about you, but I'd rather plot cosine rather than secant.

In addition to the information you have deduced, which all looks good, I like to look at the y-intercept, and find some points where the cosine is 1, where it's -1, and where it's zero.

For the y-intercept, set x=0 → y = cos(3(0)-π) = cos(-π) = ?

To find where cos(θ) = 1, of course an obvious place is where θ = 0, so that's 3x-π = 0. But in general cos(θ) = 1, where θ is an integer multiple of 2π. Of course you can generate these in terms of x, by using the easy case of the x which satisfies 3x-π = 0, and then using your information on period.

You can do similar for the the values of x which make cos(3x-π) equal to -1 and equal to zero. You can also generate these values from the information in the above paragraph, and then using the fact that the cosine is equal to -1 at 1/2 a period on either side of where it is +1. The zeros occur 1/4 of a period on either side of where it is +1.

Once you have cos(3x-π), then sketch sec(3x-π), then stretch that vertically to get y=2sec(3x-π).

3. Dec 25, 2011

Hitchens

A good way to check your graphs is this (after you've made an attempt of course!).

4. Dec 26, 2011

nando94

Thanks SammyS. I orginally planned to graph 1/cos which was the secant but it made it more confusing lol. Now I see what you mean by graph cos first.

My question is that can I also apply to secant and graph sine first or cotangent and graph tangent first? Im gonna have all three of those on my test as well.

5. Dec 26, 2011

Hitchens

Naturally, yes.

6. Dec 26, 2011

eumyang

I don't think you really want to "apply to secant and graph sine first."

7. Dec 26, 2011

nando94

lol cosecant but thanks cause now im gonna ace this test.