# Tutor.com Trigonometric Functions Session

##### Jan. 16, 2013

Session Transcript - Math - Trigonometry, 12/13/2012 6:54PM - Tutor.comSession Date: 12/13/2012 6:54PM
Length: 20.8 minute(s)
Subject: Math - Trigonometry

System Message
[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Guest (Customer)
[00:00:00] y=tan(x+ pi/2)

William B (Tutor)
[00:00:05] Welcome to Tutor.com ! Let's get started.

Guest (Customer)
[00:00:51] hello

William B (Tutor)
[00:00:53] I've written down the equation you typed. What does your assignment ask you to do with this equation?

Guest (Customer)
[00:01:21] graph from zero to 2pi but theres a phase shift

William B (Tutor)
[00:01:46] Ok! Let's see if we can graph this.
[00:02:08] When you face problems like this, do you normally make a table of x and y, and then plot the points?

Guest (Customer)
[00:02:14] nope

William B (Tutor)
[00:02:24] That's how I normally do it (if I don't have a calculator. )
[00:03:21] Ok, looks like tan(x).
[00:03:41] Now, when we have a phase shift (adding something to x),

Guest (Customer)
[00:03:48] now how could you do that with a shift

William B (Tutor)
[00:04:22] It has the same effect as adding a number to x in ANY function:

Guest (Customer)
[00:04:40] but we dont know any numbers for tan just pi and 2pi

William B (Tutor)
[00:05:01] It shifts the entire plot over by that number, to the left.
[00:05:05] Here's an example:

Guest (Customer)
[00:05:50] so how would that look in our graph

William B (Tutor)
[00:06:23] Basically we take every point on the x axis,
[00:06:36] and subtract pi/2. That will shift it to the left by pi/2.

Guest (Customer)
[00:06:55] so can you draw those off my figure?

William B (Tutor)
[00:07:19] You don't even really need to redraw your figure, just relabel the x-values you've written.
[00:07:41] So as is,
[00:07:46] This is a plot of tan(x).
[00:07:54] To make it into a plot of tan(x + pi/2),
[00:08:10] We just need to scoot the ENTIRE thing to the left, by an amount pi/2.

Guest (Customer)
[00:08:10] so they techincally dont move

William B (Tutor)
[00:08:52] Well, they do move. But they don't change shape or anything. Let me give you an example of what I mean:

Guest (Customer)
[00:10:05] so with the tan they dont move enough as to where the new graph wouldnt change?

William B (Tutor)
[00:10:29] Every x value has pi/2 subtracted from it.
[00:10:34] Another way to say that:
[00:10:41] The graph is shifted to the left by pi/2.
[00:10:52] Those two statements are actually saying the same thing.

Guest (Customer)
[00:11:02] but i dont get how we dont have to graph new points

William B (Tutor)
[00:11:10] I'll show you:
[00:11:40] What's pi minus pi/2?

Guest (Customer)
[00:12:02] pi

William B (Tutor)
[00:12:30] pi minus zero is pi. What if we subtract pi/2 from it?

Guest (Customer)
[00:12:53] ??

William B (Tutor)
[00:13:28] pi - pi/2 = ??

Guest (Customer)
[00:13:52] yea

William B (Tutor)
[00:14:11] What is pi - pi/2?
[00:14:52] If you had a pie, like a literal apple pie, and then you ate half of it, how much would be remaining?

Guest (Customer)
[00:15:28] 1/2
[00:15:34] pi/1
[00:15:36] pi/2

William B (Tutor)
[00:15:39] Right!
[00:15:59] So we had labeled a point on our graph "x = pi".
[00:16:07] But now that we're subtracting pi/2 from everything,

Guest (Customer)
[00:16:07] 0ok

William B (Tutor)
[00:16:11] What's that new x-value?

Guest (Customer)
[00:16:46] pi/2

William B (Tutor)
[00:16:50] That's right!
[00:17:07] What about the point we labeled "x = 2pi"?

Guest (Customer)
[00:17:26] 3pi/2

William B (Tutor)
[00:17:30] Bingo!

Guest (Customer)
[00:17:43] so those are the new points

William B (Tutor)
[00:18:05] Right. We've sort of shifted the x-axis over, since when we add stuff to x,
[00:18:14] It shifts our plot to the left by the same amount.

Guest (Customer)
[00:18:19] ok i got it now
[00:18:21] I got it! Thanks!

William B (Tutor)
[00:18:26] Awesome!
[00:18:38] What if we were asked to plot tan(x-pi/2)?

Guest (Customer)

William B (Tutor)
[00:19:45] Right! You'd add pi/2 to each x-value, not subtract. The plot would shift to the right, instead of the left.
[00:19:48] You've got this.

Guest (Customer)
[00:19:51] yep

William B (Tutor)
[00:19:56] Do you have any questions about anything we did today?

Guest (Customer)