# Math Help - Trouble finding reference angles with radians

1. ## 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?

2. ## Re: Trouble finding reference angles with radians

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?

3. ## Re: Trouble finding reference angles with radians

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

4. ## Re: Trouble finding reference angles with radians

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

5. ## Re: Trouble finding reference angles with radians

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?

4pi/5 ?

7. ## Re: Trouble finding reference angles with radians

How did you get that?

8. ## Re: Trouble finding reference angles with radians

pi-pi/5=4pi/5

9. ## Re: Trouble finding reference angles with radians

whoaa, wait..it is pi/5 which is 36 degrees ... right ?

10. ## Re: Trouble finding reference angles with radians

5pi/12, which is 75 degrees

11. ## Re: Trouble finding reference angles with radians

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 $\rho=2\pi-\theta$.