*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, 360*^{o}/2pi^{r}=theta^{o}/theta^{r}, which could be used to covert radian to degrees or vice-versa.*This could also be reduced to 180 degrees/(pi)radian=theta*^{o}/theta^{r }.*To find how many degrees is 2 radians, we would replace theta*^{r }with 2 using the formula above and cross multiply. So theta=180*2^{r}/ (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.*

*Arclengths -another new thing we learned.*

*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 = theta*^{o}/a , or 180/(pi)r=theta^{o}/a

*Another sample question:*

*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=theta*^{r}*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!

I love your reflections! Your perpetual enthusiasm is contagious not annoying! I will continue following both of your blogs with interest.

ReplyDeleteAm I allowed to tweet out the link to your amazing blog to my twitter followers? I am sure that we can get Darren Kuropatwa to comment!! (Just thought I would throw in his name one more time!)

Sure, Dianne, tweet away! Hey, you never know! And thanks again for all your support!

ReplyDeletewoo hoo - the power of twitter at work!!!! Let me know how many new followers you get this week :)

ReplyDelete