WHITE BOARDS!!!
Find the missing Angles and sides of each triangle
Find the missing Angles and sides of each triangle
Only 1st 2
Notice we went from triangles to now we are looking at a circle.
The 1st thing they have in common are those angles. Zoom in on what you know... Degrees in red...
Do the degrees make sense? Half a circle 180 degrees? Full circle 360 degrees?
Radians are in blue and have pi in them. Think of the circumference of a circle. The distance around a circle
C=2pi r. (Sorry I cannot make the pi symbol here.)
Recognize that one full circle is 2pi next to 360.
Half is pi next to 180. Divide 2pi by 2 you have 1pi...
All that is happening is that they are taking 2pi (one full circle) and cutting it into pieces. Start at 0. pi is at 180. Half of pi is at 90. Follow all the way around 0, half pi, one more half is 1pi, one more is 3pi divided by 2, one full circle would be 4pi divided by 2... which is 2pi.
The 1st thing they have in common are those angles. Zoom in on what you know... Degrees in red...
Do the degrees make sense? Half a circle 180 degrees? Full circle 360 degrees?
Radians are in blue and have pi in them. Think of the circumference of a circle. The distance around a circle
C=2pi r. (Sorry I cannot make the pi symbol here.)
Recognize that one full circle is 2pi next to 360.
Half is pi next to 180. Divide 2pi by 2 you have 1pi...
All that is happening is that they are taking 2pi (one full circle) and cutting it into pieces. Start at 0. pi is at 180. Half of pi is at 90. Follow all the way around 0, half pi, one more half is 1pi, one more is 3pi divided by 2, one full circle would be 4pi divided by 2... which is 2pi.
Cut pi into 4 equal sections. Look at the radians
1 section away from 0 is pi/4...
2 sections away from 0 is 2pi/4 which reduces to pi/2...
3 sections away is 3pi/4,
then 4pi/4 = pi, then 5pi/4, 6pi/4, 7pi/4 until 8pi/4 one full circle = 2pi.
1 section away from 0 is pi/4...
2 sections away from 0 is 2pi/4 which reduces to pi/2...
3 sections away is 3pi/4,
then 4pi/4 = pi, then 5pi/4, 6pi/4, 7pi/4 until 8pi/4 one full circle = 2pi.
Cut pi into 3 equal sections. Look at the radians
1 section away from 0 is pi/3...
2 sections away from 0 is 2pi/3,
3 sections away is 3pi/3 = pi,
then 4pi/3, then 5pi/3, 6pi/3 one full circle = 2pi.
1 section away from 0 is pi/3...
2 sections away from 0 is 2pi/3,
3 sections away is 3pi/3 = pi,
then 4pi/3, then 5pi/3, 6pi/3 one full circle = 2pi.
Same thing if we cut pi into 6 pieces. travel all the way around the circle all divide by 6.
This is how we get back to triangles. We can draw right triangles in any quadrant. We would then find Sine, Cosine and Tangent. Then solve...
Go to myopenmath do the intro to radians problems
This video explains what a radian measure is. Just watch the 1st 5 mins.