Given that there are 360 degrees in a circle, how many degrees would be contained in a sixth of the circle?
60 degrees
100
What are the three primary trigonometric ratios?
Sine, Cosine, Tangent
100
For which values of x between 0 and 360 degrees is sin(x) equal to ZERO?
x = 0 degrees, x = 180 degrees
100
How would the graph of y = sin(x) + 3 compare to the graph of y = sin(x)
Graph would be shifted up 3 units.
100
What does the abbreviation RPM represent?
Revolutions per minute
200
What is the relationship between the radius of a circle and its circumference?
The circumference of a circle is 2(pi) times its radius.
200
What popular mnemonic device to we use to remember which parts of a right triangle are related in each of the three primary trig ratios?
SOH CAH TOA
200
Given that sin(30) = 1/2, what other angle measure will give the same sine value?
x = 150 degrees
200
Suppose the function y=sin(x) is transformed to y=sin(x+1). What effect will this have on the graph?
Graph would be shifted one unit LEFT
200
Suppose a gear in a machine revolves at a speed of 125rpm. How many revolutions will the gear have made in one half hour?
3,750 revolutions
300
A radian is another one to describe measures of angles relative to lengths of the circle. A radian is defined as the distance around a circle spanned by the length of its radius. Based on this definition, how many radians should there be in one complete revolution around the circle?
2(pi) radians
300
Given the figure provided on the board, assume sin(x) = 4/5. Find the length of the missing side.
3 units
300
On the graph of y = sin(x), what is the range of values that y can take on?
Values will range between -1 and 1, inclusive.
300
For y = sin(x), the values of y typically range between -1 and 1. What values of will y range between for y = 5sin(x)?
Values of y range between -5 and 5.
300
Suppose a tire on a car has a diameter of 17 inches. If the car is moving forward at a rate where the tire revolves at 500rpm, how many linear feet will the tire have spanned in the course of a minute?
About 53,407 feet.
400
Convert the measure 225 degrees into radian measure.
(Hint: your final answer will be some multiple of pi!)
5(pi)/4 radians
400
Given a right triangle with a given reference angle x, for which cos(x) = 5/12, find the measure of the reference angle to the nearest whole degree.
x = 65 degrees
400
Give a rough sketch of the graph of y = sin(x) for values of x between 0 and 360 degrees.
Refer to sketch provided on board.
400
The standard period of y=sin(x) is 360 degrees (or 2pi radians). What would be the expected period of y=sin(3x)?
Period is 120 degrees (or 2(pi)/3)
400
Suppose a circle has a radius of 4 inches. What would be the length of the arc swept out on the circle that has a central angle of (pi)/2 radians?
12.57 units
500
Give all measures of angles x, in radians, for which sin(x) = 1/2.
x = (pi)/6, x = 5(pi)/6
500
For which angles x , between 0 and 360 degrees, will sin(x) = cos(x)?
45 degrees, 135 degrees, 225 degrees, 315 degrees
500
Given that sin(x) and cos(x) are related, how might their graphs be related?
Exact same shape, but the graph of y = cos(x) will be shifted left (or right) by 90 degrees compared to y = sin(x).
500
Describe all transformations applied on the parent function y=sin(x) to obtain the graph of y=2sin(x+pi)+4
Vertical stretch, factor of 2; horizontal shift, pi units left; vertical shift, 4 units up
500
Given a circle with a radius of 5cm, what is the total area of a sector of that circle that sweeps out a central angle of (5pi)/4 radians?