Radian to Degrees and back
Identify aspects of a Sinusoidal Graph
Write the Equation
Linear and Angular Velocity
Miscellaneous
100
The Formula for converting radians to degrees. radians=?
radians=degrees x π/180
100
in y=2sin(5θ)+4, what is the amplitude?
The amplitude is 2.
100
Cosine function. Amplitude=1 Period=2π Phase Shift=0 Vertical Translation=0
y=cos(Θ)
100
If a wheel rotates 3 revolutions in 5 seconds, what is its angular velocity?
The angular velocity is 6π/5 radians per second.
100
What is the y value of y=sin(Θ) at the x value of 3π/2?
-1
200
7π/6
210 degrees
200
In y=2sin(5θ)+4, what is the period?
The period is 2π/5
200
Sin Function. Inverted. Amplitude=2 Period= 2 Phase Shift=π Vertical Translation=2
y=-2sin(πΘ-π)+2
200
If a wheel spins 3 revolutions in 5 seconds, and it has a radius of 3 meters, what is the average linear velocity of a point on the edge of the wheel?
18π/5 or approx. 11.3097 meters per second.
200
What is the y value of y=tan(x) at the x value of π/2?
There is no value. It is an asymptote.
300
In y=-2sin(θ-π/2)-4, how is the position of the graph changed with respect to the x and y axes? In other words, what is the phase shift and how is it moved along the y axis?
It is moved toward the positive x direction by π/2 and moved toward the negative y direction by 4.
300
Tangent Function. Amplitude=0 Period= 2π Phase Shift=0 Vertical Translation=0
y=tan(Θ/2)
300
If a wheel which was .5 meters in diameter rolled around the circumference of earth at the equator, how many revolutions would it go through? If it rolled at 5 revolutions per second, how long, in years, would it take to cover that distance? (The circumference of the earth is approximately 40,075 km. In case you forgot, there are 1,000 meters in a km.)
It would got through approximately 251798651.2 revolutions. It would take approximately 1.597 years.
300
A horizontal translation of a sinusoid is known as the _______.
Phase Shift
400
54π/3= ? degrees
= 3240 degrees
400
In x=-tan(123456789πΘ-π/45)+89, what is the period?
The period is 1/123456789
400
Tangent Function. Inverted. Amplitude=3 Period=3 Phase Shift=-2 Vertical Translation=3
y=-3tan(πΘ/3+2)+3
400
In a circle, what is the proportion of the length of that circle's radius to one radian?
1:1. (A radian by definition is the length of that circle's radius.)
400
The period and the _________ are reciprocals of each other.
frequency
500
9630 degrees = ? radians
= 107π/2
500
In one period, how many times does a standard cosine function such as y=cos(x) cross the x axis? How many times does it cross it in infinitely many periods?
Twice in one period, infinitely many times in infinitely many periods.
500
Cosine Function. Amplitude=2 Period=2π Phase Shift=0 Vertical Translation=-5 *Must be written as a Sine function, but when graphed, it should look the same.. 0_o
y=2sin(Θ+π/2)-5
500
If a wheel is rolling along the ground, and the equation for the angular displacement of this spinning wheel with respect to time is Θ(t)=4(t)+4, and the radius of this wheel is 2.5 meters, how far has the wheel rolled after 24 hours? t must be input as seconds, and the answer must be expressed in meters.
864010 Meters.
500
The ratio of the change in the central angle to the time required for the change is known as ________ velocity.
angular
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