Finding an angle??

[all_is_on27]

So I'm taking a Calculus class, and we're reviewing trigonometry. I was never taught trigonometry, so everything is brand new. MY book is no help at all, so here is the problem:
find an angle between 0 and

[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]2[FONT=MathJax_Math]π[/FONT][/FONT][FONT=MathJax_Main][/FONT][/FONT][/FONT][FONT=MathJax_Main][/FONT][/FONT]​

that's equal to

[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]13[FONT=MathJax_Math]π[/FONT][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]/[/FONT][/FONT][/FONT][FONT=MathJax_Main]4[/FONT][/FONT][FONT=MathJax_Main][/FONT][/FONT][/FONT][FONT=MathJax_Main][/FONT][/FONT]​

If you could please respond with lots of detail on how to find this answer. That way I have some idea of what to do. Thank you!

[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][/FONT][/FONT][/FONT]
[FONT=MathJax_Main]

[/FONT][/FONT]​

 

[burakaltr]

So I'm taking a Calculus class, and we're reviewing trigonometry. I was never taught trigonometry, so everything is brand new. MY book is no help at all, so here is the problem:
find an angle between 0 and

[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]2[FONT=MathJax_Math]π[/FONT][/FONT][/FONT][/FONT][/FONT]​

that's equal to

[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]13[FONT=MathJax_Math]π[/FONT][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]/[/FONT][/FONT][/FONT][FONT=MathJax_Main]4[/FONT][/FONT][/FONT][/FONT][/FONT]​

If you could please respond with lots of detail on how to find this answer. That way I have some idea of what to do. Thank you!

[FONT=MathJax_Math]π radians = 180 degrees

[/FONT]Formulation :

180/[FONT=MathJax_Math]π = DEGREES / RADIANS[/FONT]

​

 

[all_is_on27]

I'm still a little lost. Can you work it out for me please?

 

[all_is_on27]

Yes, but nothing makes sense. I'm not the best at Trigonometry. I'm much better with Algebra and graphs. I just want a nice explanation on how to find the answer.

 

[burakaltr]

I'm still a little lost. Can you work it out for me please?

There is a concept Radian which is also a measure of the angle just like degrees are.

Degrees and radians are relationed this way
,
Circumference= 2 Pi r = 360 r

r's and 2s cancel

so Pi radians= 180 Degrees

Now I ask you : If 180 Degrees is Pi radians

[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]13[FONT=MathJax_Math]π[/FONT][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]/[/FONT][/FONT][/FONT][FONT=MathJax_Main]4 = ? Degrees[/FONT][/FONT][/FONT][/FONT][/FONT]​

 

[Mrspi]

So I'm taking a Calculus class, and we're reviewing trigonometry. I was never taught trigonometry, so everything is brand new. MY book is no help at all, so here is the problem:
find an angle between 0 and

[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]2[FONT=MathJax_Math]π[/FONT][/FONT][/FONT][/FONT][/FONT]​

that's equal to

[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]13[FONT=MathJax_Math]π[/FONT][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]/[/FONT][/FONT][/FONT][FONT=MathJax_Main]4[/FONT][/FONT][/FONT][/FONT][/FONT]​

If you could please respond with lots of detail on how to find this answer. That way I have some idea of what to do. Thank you!

[FONT=MathJax_Main]

[/FONT]​

You're asked to find an angle between 0 and 2pi that is equivalent to the given angle, (13 pi)/4

You're expected to think about an angle in standard position, with its vertex at the origin and its initial side on the positive x axis.

Since 2 pi is the same thing as 1 complete revolution, you can always add or subtract multiples of 2 pi from any angle and get a "co-terminal angle" which has an equivalent measure. The terminal side of the "new" angle measure determined by adding or subtracting a multiple of 2 pi "ends up" in the same position as the original angle.

Ok...you've got (13pi)/4. How does this compare with 2pi? Is it between 0 and 2pi? Well, we could write 2pi as (8pi)/4, and (13pi)/4 is clearly larger than that. So, subtract 2pi....

(13pi)/4 - (8pi)/4

That gives you (5pi)/4, which is between (0pi)/4 and (8pi)/4, so it is between 0 and 2pi. And it is "co-terminal with" or ends in the same place as 13pi/4.

You don't need to know the relationship between degrees and radians to do this type of problem, and you CERTAINLY do not need to convert from one unit of measure to the other.

I hope this helps you.

You may want to look up "co-terminal angles" using Google or your favorite search engine.

 

[all_is_on27]

Where did you get 8pi/4?

 

[Mrspi]

Where did you get 8pi/4?

Since the angle you were given to work with was (13pi)/4, and THAT had a denominator of 4, I thought it would be easier to compare that with 2pi if we wrote 2pi as a fraction whose denominator was 4 also.

2pi is the same as 2pi/1, right?

If I want that fraction to have a denominator of 4, I can multiply both numerator and denominator by 4:

4(2pi)
-------
4(1)

That gives (8pi)/4.

Some of that stuff you learned in elementary school will be useful throughout the rest of your "mathematical life."

Edited to add: If you have never had any trigonometry, and if writing 2pi as (8pi)/4 is confusing, I suggest you discuss your placement in calculus with your academic advisor! It is probably still early enough in the school year to be moved to a more appropriate math class.

 

[Someone2841]

So I'm taking a Calculus class, and we're reviewing trigonometry. I was never taught trigonometry, so everything is brand new. MY book is no help at all, so here is the problem:
find an angle between 0 and

[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]2[FONT=MathJax_Math]π[/FONT][/FONT][/FONT][/FONT][/FONT]
​

that's equal to

[FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]13[FONT=MathJax_Math]π[/FONT][FONT=MathJax_Main][FONT=MathJax_Main][FONT=MathJax_Main]/[/FONT][/FONT][/FONT][FONT=MathJax_Main]4[/FONT][/FONT][/FONT][/FONT][/FONT]
​

If you could please respond with lots of detail on how to find this answer. That way I have some idea of what to do. Thank you!

Where did you get 8pi/4?

It is important to understand the relationship between radians, degrees, and arc length.

You are most likely familiar with degrees. $\displaystyle 1\text{°} = 1/360$ of a complete circular rotation (i.e., $\displaystyle 360\text{°}$).

Radians give an angle in terms of arc length. $\displaystyle 1\text{ radian}$ is the angle which segments one radius of arc length. Since the circumference of a circle is equal to $\displaystyle 2\pi r$, the angle corresponding to a full rotation of a circle is $\displaystyle 2\pi\text{ radians}$.

Again, $\displaystyle 2\pi\text{ radians}$ is like saying the angle which would segment $\displaystyle 2\pi\text{ radii}$ of arc length. Since we know $\displaystyle 2\pi\text{ radii}$ fit into the complete circle, and $\displaystyle 360\text{°}$ represents the whole circle, $\displaystyle 2\pi\text{ radians} = 360\text{°}$.

Just like $\displaystyle k360\text{°}:k\in\mathbb{Z}$ (That is k*360° where k is an integer) is essentially the same (expect with more rotations) as $\displaystyle 360\text{°}$,

$\displaystyle 2k\pi\text{ rad} = 2\pi\text{ rad}:k\in\mathbb{Z}$. This is to say, $\displaystyle 2\pi\text{ rad}$ is one rotation, $\displaystyle 4\pi\text{ rad}$ is two rotations, $\displaystyle 6\pi\text{ rad}$ is three rotations, etc.

So, asking you to find an angle within the interval \(\displaystyle [0,\2pi)\) is like asking you to find an angle within that first rotation that reaches the same point in the circle as the angle that has rotated more than once. For example, if you were asked to find an angle within the interval $\displaystyle [0,360\text{°})$ that is equal to $\displaystyle 800\text{°}$, you would subtract some multiple of $\displaystyle 360\text{°}$ from that angle to make that angle fall within a single rotation. In this case, $\displaystyle 800\text{°}-2*360\text{°} = 80\text{°}$.


So, in your case, you need to find an angle within the interval \(\displaystyle [0,\2pi)\) that equals $\displaystyle \frac{13}{4}\pi$ in this case, $\displaystyle \frac{13}{4}\pi - 2\pi$ will do the trick.

$\displaystyle \frac{13}{4}\pi - 2\pi = \frac{13}{4}\pi - \frac{8}{4}\pi = \frac{5}{4}\pi$

 

[mmm4444bot]

I'm taking a Calculus class, and we're reviewing trigonometry. I was never taught trigonometry

You are in the wrong class! :shock: