Radians and Degrees
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- เผยแพร่เมื่อ 20 ก.ค. 2024
- This trigonometry video tutorial provides a basic introduction into radians and degrees. It explains the definition of the radian and how to calculate the angle measure in radians given the arc length of a circle and the length of the radius. This video also explains the process of converting degrees to radians and converting radians to degrees. To convert from degrees to radians, multiply the angle measure in degrees by pi divided by 180. To convert from radians to degrees, multiply the radian measure by 180 over pi. To calculate the angle measure in radians - divide the arc length by the length of the radius of the circle. This video also explains how to draw angles in standard position using radians instead of degrees. It explains the location of common angles such as pi/4, 3pi/4, 5pi/4, and 7pi/4 and more. This video contains a lot of examples and practice problems.
Trigonometry - Basic Introduction:
• Trigonometry
Introduction to Angles:
• Introduction to Angles
Radians and Degrees:
• Radians and Degrees
What Exactly Is a Radian?
• Trigonometry - What Ex...
Coterminal Angles:
• Coterminal Angles In R...
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Decimal Degrees to DMS:
• Decimal Degrees to DMS...
Arc Length of a Circle and Sector Area:
• Arc Length of a Circle...
Linear Speed and Angular Velocity:
• Linear Speed and Angul...
Clock to Angle Problems:
• Clock Aptitude Reasoni...
The Unit Circle:
• The Unit Circle, Basic...
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A little tip about converting radians to degrees,ex. 2 pi All over 3 x 180° All over pi. Simply cancel the two pi's then 180 ÷ 3 × 2 = easy to answer
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Quick mechanical tip: to convert any angle from degrees to radians, divide that angle by 180. You will get a fraction, now write pi next to whatever number is in the numerator and boom, there is your angle in pi radians. And if you have 1 in the numerator, change it to pi. For example, if you need to convert 450° degrees to pi radians, divide 450/180, you will get 5/2. Now write pi next to 5 in the numerator, and there is your answer. And if you need to convert 30° to pi radians, do the same, you will get 1/6, and just substitute that 1 with pi. The best thing about this method is that it requires no thinking and is extremely fast. I still recommend taking the time to understand how the conversion works, but once you've done that, this method will save you a lot of time, as it works for less common angles just as well.
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There are three modes in calculator for doing trig. and inverse trig. functions, which are degrees (deg), radians (rad), and gradians (grad). Somehow, we don't talk about gradians much in math, physics, or engineer class. I know there is a conversion between gradians with degrees and radians.
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At 3:00: interesting approach to explain, why there maybe a „unit“ rad. But I wouldn‘t do it. It isn‘t necessary as well.
Because the length of the radius isn‘t 6 cm/radius but simply 6 cm. Or you had to insert 12cm/arc as well, which inserts nice explanations to the formula, but likewise is not intended by SI.
The units given in SI are m/m, this cancels out. So an angle in radians is a pure number. SI makes it possible to use „rad“ as an „unit“, too. But this I call a reminder-unit, which you can/have to replace by a 1 (that means, ignoring it) to get to the „real“ result.
The problem with „rad“ is, that people look at it as „real“ unit, and units you should never loose. But this „unit“ is supposed to be lost, resp. interchanged by a 1.
Thankyou so much for clearing. I got confused when he said 6cm per radius.
How do you know which factors it is in each problem that equal 180
Even though I'm watching this in 2021...I wanna say thank you alot this video help me in many ways...Plus I have a trig test tmr TY
5:25, i actually figured out the formula for this many days ago when i was copying notes from the powerpoint presentation that my teacher sent to me and my class and saw our teacher's examples from the presentation. Of course, i did a bit of my own research first just to figure out the formula.
Very good lecture. But I thought is this valid for any cirkel, let say on with r=7.
I found yes as e.g. the half cirkel with r= 7 is 2(pi)r= 2(pi)7. As radians is the segment divided by the radius,
in this case, we would get2(pi)7/7 that will become 2(pi). It would have been good to clarify that. Fortunately I had some old knowledge in my luggage. Thank you anyway. Your way of explaining is great with your calm voice and moderate tempo. Retired math teacher talking. Have a good day.
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