Today in class we grappled with the problems from the end of section 4.1 about arc length, angular speed, and linear speed (with unit changes for distance and time included).
All agreed that this was tricky. Examples were attached to the last blog. We took a 10 pt quiz over this at the end of class (much to the chagrin of all).
The most important take-away from that part of the lesson:
arc length (s) = radians time radius. This is the only part of the lesson that will be used in the next new content. It comes from the idea that in geometry we described arc length as part of a circumference = angle/360 times 2 Pi r. But when we switch to radians, it becomes radians/2 Pi times 2 Pi r and the 2 Pi's cross out, yielding radians times radius. This is important to developing understanding of the unit circle next week.
We spent quite a bit of class time recording and figuring out information about the degrees, radians, and coordinates of all the angles that are multiples of 45 and 30 degrees of rotation from standard position. Our approach was to use the 30-60-90 and 45-45-90 shortcuts from geometry. Just before the quiz, Ms. Bogart demonstrated the connection to the trig ratios from geometry to these special coordinates in the unit circle. That is where we will begin class on Monday. HOMEWORK IS TO ACCURATELY RECREATE THIS INFO ON THE BACK OF THE BLUE HANDOUT.
I am also recommending that you watch the Khan Academy video linked below. It does a great job of connecting to the idea that I touched on before the quiz and will put you in the correct mindset for the warm-up. Attached below are links to a blank unit circle, a completed unit circle, and the Khan video.
All agreed that this was tricky. Examples were attached to the last blog. We took a 10 pt quiz over this at the end of class (much to the chagrin of all).
The most important take-away from that part of the lesson:
arc length (s) = radians time radius. This is the only part of the lesson that will be used in the next new content. It comes from the idea that in geometry we described arc length as part of a circumference = angle/360 times 2 Pi r. But when we switch to radians, it becomes radians/2 Pi times 2 Pi r and the 2 Pi's cross out, yielding radians times radius. This is important to developing understanding of the unit circle next week.
We spent quite a bit of class time recording and figuring out information about the degrees, radians, and coordinates of all the angles that are multiples of 45 and 30 degrees of rotation from standard position. Our approach was to use the 30-60-90 and 45-45-90 shortcuts from geometry. Just before the quiz, Ms. Bogart demonstrated the connection to the trig ratios from geometry to these special coordinates in the unit circle. That is where we will begin class on Monday. HOMEWORK IS TO ACCURATELY RECREATE THIS INFO ON THE BACK OF THE BLUE HANDOUT.
I am also recommending that you watch the Khan Academy video linked below. It does a great job of connecting to the idea that I touched on before the quiz and will put you in the correct mindset for the warm-up. Attached below are links to a blank unit circle, a completed unit circle, and the Khan video.