Converting Angles
Arc Length
6 Trig Functions
Periodicity
Damping Factor
Inverse Trig
100
What do you multiply be to convert degrees to radians?
pi/180
100
What is the formula for arc length?
s=(pi*r*theta)/180
100
What is the opposite/ reciprocal of sin?
csc
100
What does the concept of periodicity tell us about angles beyond 0 to 2pi
They always have an equivalent angle between 0 and 2 pi
100
What is damping factor? What does it do?
A function multiplied in front of a sin or cos function that guides how the trig function oscillates
100
What is an inverse trig function asking for?
The angle given the ratio
200
What do you multiply to convert radians to degrees?
180/pi
200
Find the arc-length of a 45-degree sector cut from a circular disc of radius 6 inches.
4.71
200
What is the opposite/ reciprocal of cos?
sec
200
How do you find the equivalent angle?
divide the angle by 2pi
Multiply the full decimal by 2pi without the whole # to see how far past a full rotation it goes
200
How do you graph a damped oscillation?
Graph the positive and negative damping factors, then oscillate between
200
sin^-1(1/2)
pi/6(30)and (5pi)/6(150)
300
Convert 60o to radians
pi/3
300
Find the arc-length of a 37-degree sector cut from a circular disc of radius 2 inches.
1.29
300
Find sin and csc
sin(theta)=12/15
csc(theta)=15/12
300
Simplify with the ideas of periodicity
sin((237pi)/4)
sin((5pi)/4)=-sqrt2/2
300
Identify the damping factor of the damped oscillation function xcos(3x) and graph.
damping factor is x
300
arcsin(-sqrt2/2)
(5pi)/4(225),(7pi)/4(315)
400
"Convert " (5pi)/6 " to degrees"
150o
400
You're riding on a carousel. The radius of the carousel is 20 feet. How far will you travel to get halfway around?
Halfway = 180o
62.83 ft400
Find cos and sec
cos(theta)=9/15
sec(theta)=15/9
400
Simplify with the ideas of periodicity
sin((19pi)/2)
sin((3pi)/2)= -1
400
Identify the damping factor of the damped oscillation function x2sin(2x) and graph.
damping factor is x2
400
A zipline is 70 ft long and starts at the top of a 40 ft tall tree. What is the angle of the drop for the zipline? Round to the nearest degree.
about 55o
500
Convert
(2pi)/9 "to degrees"
40o
500
How much crust is on a slice of pizza if the pizza has a diameter of 10 inches, and it's cut into 8 slices?
r=5
angle : 360/8 = 45
3.93 in
500
Find tan and cot
tan(theta)=12/9
cot(theta)=9/12
500
Simplify with the ideas of periodicity
cos((1457pi)/3)
cos((5pi)/3)= 1/2
500
Identify the damping factor of the damped oscillation function |x|sin(6x) and graph.
damping factor is |x|
500
A building that is 60 feet tall casts a shadow along the ground that is 85 feet long. What is the angle of elevation, A, of the sun? Round to the nearest degree.
~~35^o