Today in class, we continued our lesson on radians and degrees, and how to convert from one to another.
- We know that the number of degrees in a circle is 360, and the number of radians in a circle is 2(pi).
- So then, we have a proportion, 360o/2pir=thetao/thetar , which could be used to covert radian to degrees or vice-versa.
- This could also be reduced to 180 degrees/(pi)radian=thetao/thetar .
- To find how many degrees is 2 radians, we would replace thetar with 2 using the formula above and cross multiply. So theta=180*2r / (pi) , would come to approximately 114.6 degrees.
- To be exact, just multiply 180*2, leave pi as is, and we get 360/(pi).
- To find how many radians is in 30 degrees, replace 30 by theta degrees instead, which I’ll leave you to figure out – exact or approximate amount.
- If we have an angle, we get an arc or a section of the circumference. This is called the arclength.
- And the bigger the angle, the bigger the arclength. :O
- If we take 360 degrees of the circle, the arclength would then be the whole circle, or its circumference. And its formula is C=2(pi)r.
- a (arclength) = 2(pi)r when theta=360. From this, we get a proportional formula similar to the one with radians.
- 360 degrees/2(pi)r = thetao/a , or 180/(pi)r=thetao/a
- If we had r=5cm, and an angle=45 degrees, find the arclength subtending this angle. Mrs. McGoldrick also gave us a formula for arclength: a=thetar*r , but it can only be used in radians.
Hope you all have a radiant rest of the day.
- She didn't leave any content or formulas out
- She put in subtitles
- She asked not one, but two questions
- Her personality came through, especially at the end with the "radiant day"!
- The clarity of it suggested to me that it was a pretty well-done lesson (pat on the back for Audrey)
- diagrams - slides from the lesson or their own
- colour coding
- worked out examples
- math notation - how the heck do you get that into a blog post - to find out
Today's lesson was on the unit circle. Introduction to. Here's the powerpoint for the lesson that Shelley will be blogging about this weekend (lucky girl!):
feb 4 unit circle intro
I know....97 slides! But don't worry, that's only because I show each little step.....you'll see. Enjoy!