Trouble finding reference angles with radians

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Apr 13th 2013, 04:02 PM
davecolombia

Trouble finding reference angles with radians

I am having trouble finding reference angles with radians. For instance: #1) 33pi/4
#2) -23pi/6
How do I go about solving these?
Apr 13th 2013, 04:41 PM
Plato

Re: Trouble finding reference angles with radians

Quote:

Originally Posted by davecolombia

I am having trouble finding reference angles with radians. For instance: 33pi/4 -23pi/6 How do I go about solving these?

Please do not be insulted by this remark: often it is a problem in basic arithmetic.

$\frac{33\pi}{4}-\frac{23\pi}{6}=\frac{99\pi}{12}-\frac{46\pi}{12}=\frac{53\pi}{12}=4\pi+\frac{5\pi} {12}$ .

Now we can disregard all even multiples of $2\pi$ .

Thus in this case we endup with $\frac{5\pi}{12}$ .

What is the reference angle there?
Apr 13th 2013, 04:44 PM
davecolombia

Re: Trouble finding reference angles with radians

I apologize, I have written them wrong...they are separate questions: #1. 33pi/4 #2. -23pi/6
Apr 13th 2013, 04:47 PM
davecolombia

Re: Trouble finding reference angles with radians

I apologize, I have written them wrong...they are separate questions: #1. 33pi/4 #2. -23pi/6
Apr 13th 2013, 06:51 PM
Plato

Re: Trouble finding reference angles with radians

Quote:

Originally Posted by davecolombia

I apologize, I have written them wrong...they are separate questions: #1. 33pi/4 #2. -23pi/6

The fact that your post is mistaken makes no difference.
We can disregard any multiple of $2\pi$

Here is an example.
$\frac{76\pi}{5}=15\pi+\frac{\pi}{5}=14\pi+\frac{6 \pi}{5}$ .

So disregard the $14\pi$ and get the equivalent number of $\frac{6\pi}{5}$ .

Now what is the reference angle angle?
Apr 13th 2013, 07:07 PM
davecolombia

Re: Trouble finding reference angles with radians

4pi/5 ?
Apr 13th 2013, 07:29 PM
HallsofIvy

Re: Trouble finding reference angles with radians

How did you get that?
Apr 13th 2013, 07:40 PM
davecolombia

Re: Trouble finding reference angles with radians

pi-pi/5=4pi/5
Apr 14th 2013, 10:17 AM
davecolombia

Re: Trouble finding reference angles with radians

whoaa, wait..it is pi/5 which is 36 degrees ... right ?
Apr 14th 2013, 11:07 AM
davecolombia

Re: Trouble finding reference angles with radians

5pi/12, which is 75 degrees
Apr 14th 2013, 11:55 AM
Plato

Re: Trouble finding reference angles with radians

Quote:

Originally Posted by davecolombia

5pi/12, which is 75 degrees

Here are the rules for reference angles.
First reduce to $0\le \theta <2\pi.$

The the reference angle is $\rho$ where
If $0<\theta<\tfrac{\pi}{2}$ then $\rho=\theta$

If $\tfrac{\pi}{2}<\theta<\pi$ then $\rho=\pi-\theta$

If $\pi<\theta<\tfrac{3\pi}{2}$ then $\rho=\theta-\pi$

If $\tfrac{3\pi}{2}<\theta<2\pi$ then $\rho=2\pi-\theta$ .