Associated Topics || Dr. Math Home || Search Dr. Math

### Finding Intervals in Trig Graphs

```
Date: 10/25/98 at 18:11:30
From: sara
Subject: Graphing sine and cosine functions

I'm in pre-calculus, and I don't understand graphing sine and cosine
functions. I understand it up until you have to divide the interval
into four equal parts. One of the problems I'm having a hard time with
is the interval negative pi divided by four to seven pi divided by
four. In the book, you have to add the two together and multiply by
1/4, 1/2, and 3/4. When I add the two intervals, I get six pi over
four. Then I multiply it by 1/4, and I get three pi over eight. But
```

```
Date: 10/26/98 at 12:30:44
From: Doctor Peterson
Subject: Re: Graphing sine and cosine functions

Hi, Sara. I think what you are trying to do is to divide the interval:

(-pi/4, 7pi/4)

into four equal parts. The fact that it doesn't start at zero is what
makes this difficult for you, together with the fact that the left end
is negative. I get the impression you are just trying to follow an
example that did start at zero, without thinking about what it means.
So let's start out by picturing what we're doing, rather than just
working with numbers.

---+===+===+===+===+===+===+===+===+---
-pi  0               pi         7pi
---                             ---
4                               4

First we have to measure how long the interval is. If you trust my
drawing, you can just count the eight pi/4 marks I've made. If you
don't, what you have to do is to subtract (NOT ADD!) the two ends:

7 pi    -pi   (7 - -1) pi   8 pi
---- - ---- = ----------- = ---- = 2 pi
4      4         4          4

Now if we want to divide this interval into four equal parts, each one
will be a quarter of this length:

2 pi   pi
---- = --
4     2

Now the points where you have to "cut" the interval will be every pi/2,
starting at your left end point:

-pi   pi   pi
--- + -- = --
4     2    4

pi   pi   3 pi
-- + -- = ----
4    2     4

3 pi   pi   5 pi
---- + -- = ----
4     2     4

Just as a check, the next point should be your right end point:

5 pi   pi   7 pi
---- + -- = ----      looks good!
4     2     4

So the 1/4, 1/2, and 3/4 points are pi/4, 3pi/4, and 5pi/4:

---+===+===+===+===+===+===+===+===+---
-pi  0   pi     3pi     5pi     7pi
---     ---     ---     ---     ---
4       4       4       4       4

The two mistakes you made were adding rather than subtracting, and then
stopping too soon and taking the length of 1/4 of the interval as the

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Equations, Graphs, Translations
High School Trigonometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search