Question 1

Can you possibly have negative angles?

Accepted Answer

Negative angles are clockwise angles.  (Counterclockwise is positive)

Question 2

If pi continues forever, how can we use it to define answers? That would mean every answer we get would continue on forever, but we shorten pi and thus makes none of the math we do with pi actually 100% true but rather an estimated amount. I don't even understand the concept of pi honestly. Can someone explain to me?

Accepted Answer

Take a measurement of a length of anything, we won't get an exact whole number. A pencil said to be 8 cm long may be 8.000034 cm for example. We are always estimating because the exact amount is almost never needed, and we take as accurate a measurement as required. So, every answer may continue on forever, but what we estimate, is what we need practically.

Theoretically in math, since we always use rational numbers most of the time, an irrational number like pi is often confusing as it does not provide a definite rational answer. Instead we have to estimate to the accuracy required for the situation. If you want to find the circumference of a random cart wheel, you dont need accuracy. When you find the circumference of a rocket, you may need more accuracy.

But of course, theoretically we can still get a definite answer if we just dont expand π and leave it as π. Circumference of a circle of diameter 3 is 3π. This gives you a perfect theortical answer. Otherwise it would be 3*3.14..... and as you said, it is not a perfect defined answer and is not theoretically accurate.

Hope this helps!
- Super7SonicX

Question 3

Is there any kind of notation for radians?

Accepted Answer

Yes, there is, though it is rarely used.
Usually, the no. of radians is written like 2rad
You write degrees with a little circle at the top 1.2°
Same way, an angle of 1.2 radians would be written either as "1.2 rad" or "1.2 with a "c" at the top.(I can't seem to get the 'c' using formatting here.)

See-
 http://en.wikipedia.org/wiki/Radian 
 , second paragraph last line for the answer to your question.

Question 4

Are negative degrees actual things, or are they hypothetical like negative numbers?

Accepted Answer

they are actual things. For example, if you rotate an object 90 degrees clockwise, it would be -90 degrees. Like the number line, negative and positive only show direction

Question 5

isn't -90 degrees 270 degrees?

Accepted Answer

If the reference point is the positive x axis then yes, -90 degrees is 270 degrees.

Question 6

Is 1.5 pi the same as 270?

Accepted Answer

Yep, 1.5π radians is exactly 270°.

We usually use fractions for radians, so that would be 3π/2. What you said is completely correct, though!

Question 7

Is there any other way to measure the angle just like degrees,  radians....?

Accepted Answer

There was an attempt at a metric measure of angle where the right angle was divided into 100 parts (as opposed to the usual 90 degrees). The measure was called the gradian. There were 400 gradians in a complete revolution, and 1 gradian = 0.9 degrees.

It hasn't really caught on, and the only place I've seen it is on calculators.

Is that what you had in mind?
https://en.wikipedia.org/wiki/Gradian

It hasn't really caught on, and the only place I've seen it is on calculators.

Is that what you had in mind?
https://en.wikipedia.org/wiki/Gradian

Question 8

Why did humans invent radians and degrees? Isn't one enough?

Accepted Answer

Radians make calculation easier in dealimg with derivatives.

https://qedinsight.wordpress.com/2011/03/14/why-radian-measure-makes-life-easier-in-mathematics-and-physics/

For example, if you take the derivative of sin x that will be 
pi/180 cos x using degrees however by defining pi=180 the derivative will just be cos x which is simpler. You can get the result from the proof theorem on the derivative of sin x being cos x except instead of using radians as Sal does in his calculations use degrees. You will also notice that:

lim_x->0 sin x/x doesn`t equal 1 but pi/180 from using degrees by following the steps he carries out.

To understand the proof you should, however, have an understanding of limits/differentiation  and circular geometry has in finding arc length and the area of a sector which you can learn about in some of Sal videos.

Question 9

why does Sal say, "radiussess"?

Accepted Answer

There is a debate in math education that nobody needs to be told that "radiuses" is the plural of "radius", but "radii" has to be a vocabulary word.  Since both words are acceptable plurals for "radius" in English, it would be clearer to teach with "radiuses", especially to students who don't speak English as their first language.  I get the feeling in this video that Sal is new to this debate and is being a little silly about it.  ^_^

Question 10

When I have 5pi/9 and I am converting it to degrees do I set them up in the proportion just as in the video? And just like the example with -pi/2 do I multiply the 5 by 180? My answer was 100 degrees. Would like to know if I did it right. thx!!

Accepted Answer

You are correct, 5π/9 * 180/π = 100.  Notice you could multiply 5 * 180 and divide by 9 or you could divide 180/9 to get 20 and then multiply by 5 to get 100.

Course: Algebra 2 (Eureka Math/EngageNY) > Unit 2

Radians & degrees

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