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## Integrated math 2

### Course: Integrated math 2>Unit 11

Sal discusses the general approach to converting between radians and degrees and vice versa. Created by Sal Khan.

## Want to join the conversation?

• Can you possibly have negative angles?
• Negative angles are clockwise angles. (Counterclockwise is positive)
• 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?
• 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
• Is there any kind of notation for radians?
• Yes, there is, though it is rarely used.
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-
• Are negative degrees actual things, or are they hypothetical like negative numbers?
• 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
• I like how he said radiaseseseseseseses.
• True
(1 vote)
• Is 1.5 pi the same as 270?
• 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!
• Is there any other way to measure the angle just like degrees, radians....?
• 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?
• Why did humans invent radians and degrees? Isn't one enough?
• Radians make calculation easier in dealimg with derivatives.

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.