All Flashcards
How do we know if we are going to stretch the waves of a sinusoidal function horizontally before solving for the period?
You can tell if you are going to stretch the waves before finding the period if “k” is a fraction
How do you know if you are going to horizontally compress the waves of a sinusoidal function before solving for the period?
Before solving for the period, you can tell if you are going to compress the waves of a sinusoidal function if “k” is a whole number
How do we know if we need to flip a graphed sinusoidal function?
If the value of “A” is negative, that signifies we need to flip the function along with compress or stretching the waves vertically
How do we know the value of the highest and lowest points of the sinusoidal function?
Whatever numerical number “A” is determines our highest and lowest points
When referring to the sinusoidal function formula, what does “d” stand for and what does it do to the function?
“D” signifies the vertical shift of the function. Depending on its value, the function will either shift up or down.
How do we know if a sinusoidal function should be shifted up or down?
If D > 0, we shift the function up. If D < 0, we shift the function down.
How do we know when to shift the sinusoidal function left or right?
How do we know when to shift the sinusoidal function left or right?
When referring to the sinusoidal function formula, what does “c” stand for and what does it do to the function?
“C” signifies the horizontal shift of the function. Depending on its value, the graph will either shift left or right
What is the formula to find a period?
2pi/k
When referring to the sinusoidal function formula, what does “A” stand for and what does it do to the graph?
“A” signifies the amplitude of the waves. Depending on its value, it will compress, stretch, and/or flip the waves vertically
When referring the sinusoidal function formula, what does “k” stand for and what does it do to the function?
“K” signifies the frequency shift of the waves. Depending on its value, it will compress or stretch the waves horizontally
What is a period?
A period is the shortest distance it takes a function to repeat itself
What is the formula for a sine sinusoidal function?
A*sin(k(t+/-c))+/-d
What is the formula for a cosine sinusoidal function?
A*cos(k(t+/-c))+/-d
What are sinusoidal functions?
Smooth, repetitive, wave-shaped graphical functions
What is the general shape of sine and cosine when graphed?
Waves (like sound waves)
How often do sine and cosine repeat?
They repeat every 2pi
What happens to sine and cosine with t is negative?
cos(-t) = cos(t)
sin(-t) = -sin(t)
positive
Positive: Quadrant 1 and 2
Negative: Quadrant 3 and 4
What is the domain and range for sine/cosine?
Domain = All real number
range = -1 </= t </= 1
When is cosine positive and negative?
Positive: Quadrant 1 and 4
Negative: Quadrant 2 and 3
What are the other common trig functions we use and their formulas?
Tan(t) = sin(t)/sin(t)
Cot(t) = cos(t)/sin(t)
Sec(t) = 1/cos(t)
Csc(t) = 1/sin(t)
What is the Pythagorean Identity?
(cos(t))^2+(sin(t))^2=1
What values do sine and cosine correspond to in a coordinate?
Sine = y-coordinate of P(t)
Cosine = x-coordinate of P(t)
What is the unit circle formula?
x^2+y^2=1
What are the coordinates on the unit circle for the following values:
0, pi/6, pi/4, pi/3, pi/2, pi, 3pi/2, 2pi
(1,0), (sqrt(3)/2, 1/2), (sqrt(2)/2, sqrt(2)/2), (1/2, sqrt(3)), (0,1), (-1,0), (0,-1), (1,0)
Define: Reference Number
A reference number is the shortest distance to the x-axis from the terminal point (P(t))
What is negative in which quadrant?
Quadrant 1 = no negatives, Quadrant 2 = x negative, y positive, Quadrant 3 = both negative, Quadrant 4 = x positive, y negative
What are the three main terminal points we will see?
P(pi/6), P(pi/4), P(pi/3)
What is the circumference formula?
2pi * r
What is the circumference of the circle?
2pi
What direction do you move in the unit circle?
If t is positive, you move counter clockwise; If t is negative, you move clockwise
Define: Terminal point
A terminal point is the point you end up at after moving a certain distance around the circle
What is the notation for the terminal point?
P(t) where t represents the distance moved
What is the distance formula?
d((x1,y1), (x2,y2))=sqrt((x2-x1)^2+(y2-y1)^2)
Define: Unit circle
A circle with a radius of 1 unit with the center located at the origin
