Radian Measure
What is a full rotation of a circle in radians?
2pi
What is the the equation to find the length of an arc in radians
Arc=rtheta
What is the equation of the area of a sector of a circle in radians
Area =(1/2)thetar^2
Gear 1: radius 12 cm, rotates pi/3
Gear 2: Radius 4 cm, how much does it rotate?
Gear 1 Arc:
12cm*pi/3=4pi cm
Gear 2:
4pi cm=theta*4cm=>theta=pi
What was the first day of covid lockdown (in California)
March 19, 2020 or 3/19/20
What are the equations to turn radians into degrees and degrees into radians
deg to rad: deg*pi/180=rad
rad to deg: rad*180/pi=deg
Find the length of an arc of a circle with radius 12 inches and has a central angle of
(5pi)/3 radians
Arc = (5pi)/3(12)=20pi inches
If the central angle of a circle is (5pi)/6 and has a radius of 6 ft, what is the area of the sector?
Sec=1/2*(5pi)/6*(6ft)^2=>15pi ft^2
If SF is (4pi)/9 degrees north, and LA (is terrible) (5pi)/36 degrees north, what is the distance between them if the earth has a radius of 6400 km
((4pi)/9-(5pi)/36)*6400=2133pi km
What is the population of SF?
~810 thousand
What is
(5pi)/6
in degrees?
150
Find the radius of a circle if the length of the arc is
50pi ft
and has a central angle of
(5pi)/4
Draw the circle!
50pift=(5pi)/4theta=>40 ft
Given the area of a sector is
36ft^2
and the radius is 3 ft - what is the central angle?
36pift^2=1/2theta(3ft)^2=>theta=8pi
Find the missing piece of information:
Gear 1: r=8 cm , theta=(7pi)/4
Gear 2: r=?, theta = 4pi
(hint - use the arc lengths to help you)
Gear 1 arc length:
Gear_1=rtheta=8*(7pi)/4=14pi
Gear_2:14pi=4pir=>r=7/2 cm
Draw Mr. Weatherly in 20 or 40 years from now.
Please no gravestones :(
Find a negative and positive angle that are coterminal with
(2pi)/3
-(4pi)/3 and (8pi)/3
Find the central angle of an arc that measures 100pi cm with a radius of 15 cm.
Draw the circle!
100picm=theta*15cm=>theta=(20pi)/3
what is the radius of circle given the area is
100 pi ft^2
and the central angle is (2pi)/3 degrees.
hint hint: Simplify nicely!!!
100pift^2=(1/2)(2pi)/3r^2=>r=10sqrt3 ft
If NY is pi/3 radians north and Sao Paulo is pi/6 radians south, what is the distance between them if the radius of Earth is 6400 km?
Arc=(1/2)(pi/3+pi/6)(6400)=3200pi mi
translate these symbols: alpha, beta, theta, delta, mu
alpha, beta, theta, delta, mu
Through how many radians does the hour hand of a clock rotate in 24 hours? What about the minute hand?
Hour: (2 rotations)/1*(2pi radians)/(1 rotation)=4piradians
Minute: 24 rotations*(2piradians)/(1 rotation)=48pi radians
Name the first 3 elements
Hydrogen, Helium, Lithium