1. [SOLVED] Trig Function Graphs

Hello, I'm new here and this is my first post, but let me get right to the problem.

I have several functions to graph. Explanations are appreciated, I'm not looking to just get answers.

1.) y = tan (2$\displaystyle \theta$ + $\displaystyle \pi$) + 1

2.) y = cot ($\displaystyle \theta$/2 - $\displaystyle \pi$/2) - 2

3.) y = csc $\displaystyle \theta$ + 3

4.) y = sec ($\displaystyle \theta$/3 + $\displaystyle \pi$) - 1

Any help is appreciated. Thank you.

2. #3 isn't clear.

2) Rewrite to expose the characteristics.
3) Redraw with one characteristic at a time.

The first

y = tan (2( + /2)) + 1

y = tan (2( - (-/2))) + 1

y = tan () -- Draw this

y = tan () -- Draw this. What happens to the PERIOD?

y = tan (2( - (-/2))) -- Draw this. What happens HORIZONTALLY?

y = tan (2( - (-/2))) + 1 -- Draw this. What happens VERTICALLY?

Go for it!

3. Originally Posted by TKHunny
#3 isn't clear.
I am not sure. This is what is written on my paper, but my teacher does make a lot of errors. I apologize.

As for 1)

I'm understanding the separation you are doing in the first 2 steps.
In this step:

Originally Posted by TKHunny
y = tan () -- Draw this
How can I draw the graph if I have no value for $\displaystyle \theta$?

I believe i forgot to mention im given a graph with x values ranging from $\displaystyle -\pi$ to $\displaystyle \pi$
and y values ranging from 4 down to -2.

Thank you.

EDIT: Alright, I think I understand now. I completely forgot the graph of tan $\displaystyle \theta$ for some reason. Too late for my brain heh. Anyway, I got the horizontal shift of -$\displaystyle \pi$/2 and the + 1 vertical shift. Although I'm not sure about the 2. This is a vertical stretch?

4. Originally Posted by Heiwa
Although I'm not sure about the 2. This is a vertical stretch?
y = tan(x)

y = b*tan(x) -- Vertical Stretch (b>1)/Shrink(0<b<1)

y = tan(b*x) -- Horizontal Stretch/Shrink

5. Oh yes I see now. I actually asked my teacher today. Thanks for the help.
+thanks.