Sine
How do we find the period for our Sine functions if they are in the form
y=asin(b(x-h))+k
period = (2pi)/b
How do we find the amplitude for our cosine functions if they are in the form
y=acos(b(x-h))+k
|a|
What trigonometric function is used as a guide to graph a secant function?
use the reciprocal of secant which is cosine
What is the range of all tangent and cotangent functions?
(- oo, oo)
What is the maximum sea level on a beach when the sea level in feet is modeled with the equation
f(t)=5.14sin(pi/6(x-1.5))+21.33
21.33 + 5.14 = 26.47 feet
Where is the starting point of the Sine graphs when there are no vertical or horizontal shifts?
the origin, (0, 0)
Where is the starting point of the original cosine graph?
(0, 1)
Where do the vertical asymptotes of sec and csc occur in relation to their guide function?
Vertical asymptotes on sec and csc graphs occur where their guide function crosses the midline.
How would you find the placement of a vertical asymptote for the equation
y=atan(b(x-h))+k
Solve for x when
b(x-h)=pi/2
What is the minimum sea level on a beach when the sea level in feet is modeled with the equation
f(t)=5.14sin(pi/6(x-1.5))+21.33
21.33 - 5.14 = 16.19 feet
What is the Amplitude of this function?
y=-3sin(pix-pi)
a = 3
What is the Period of this function?
y=-3cos(pix-pi)
2
Where are the vertical asymptotes on the original cosecant function graph?
For all integers n, the vertical asymptotes will appear where
x=npi
After finding the 1st x-value for a table of 5 points, how do you find 4 more x-values to graph a whole period?
Divide the period by 4 and add this to each x-value to get the next x-value for the table of 5 points.
If t is measured in hours, what is the period of the equation
f(t)=5.14sin(pi/6(x-1.5))+21.33
12 hours
For a table of 5 points, what should the starting x-value be for this function?
y=2sin(2(x-pi/2))+5
pi/2
What is the y-intercept of the function
y=2cos(2pix)-5
(0, -3)
Where are the vertical asymptotes in one period of the function
y=4csc(x/2)+3
x=0, x=2pi, and x=4pi
Where are the vertical asymptotes on either side of the y-axis for the graph of
y=1/2tan(x/4)
x=-2pi and x=2pi
If t is measured in hours after midnight, what time is it at the first high tide after midnight for the equation
f(t)=5.14sin(pi/6(x-1.5))+21.33
4:30 AM (Start at a t-value of 1.5 which is 1:30 AM and add 3 hours to get 4:30 AM. The period of 12 hours divided by 4 is 3 hours. Sine starts at its midline and rises to high tide after 3 hours.)
What is the range in y-values for this function?
y=-4sin(2pix)+1
[-3, 5]
What is the range of the function
y= -1/2 cos(2x-pi) + 7
[6.5, 7.5]
What are the y-values for the bottom of the u-shaped curves and the top of the upside-down u-shaped curves on the graph of the function
y=3sec(2pix-pi)
The bottom of the u-shaped curves will appear at y=3 and the top of the upside-down u-shaped curves will occur at y=-3.
With a period of 2pi, and vertical asymptotes at x=0 and x=2pi, what ordered pairs should be used for the 3 middle points for the graph of
y=-2cot(x/2)+1
(pi/2, -1), (pi, 1), and ((3pi)/2, 3)
If t is measured in hours after midnight, what time is it at the first low tide after midnight for the equation
f(t)=5.14sin(pi/6(x-1.5))+21.33
10:30 AM (Start at a t-value of 1.5 which is 1:30 AM and add 9 hours to get 10:30 AM. The period of 12 hours divided by 4 is 3 hours. Sine starts at its midline and rises to high tide after 3 hours, then back to midline after 6 hours, then low tide after 9 hours.)