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Question 1

How do we know if we are going to stretch the waves of a sinusoidal function horizontally before solving for the period?

Answer 1

You can tell if you are going to stretch the waves before finding the period if “k” is a fraction

Question 2

How do you know if you are going to horizontally compress the waves of a sinusoidal function before solving for the period?

Answer 2

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

Question 3

How do we know if we need to flip a graphed sinusoidal function?

Answer 3

If the value of “A” is negative, that signifies we need to flip the function along with compress or stretching the waves vertically

Question 4

How do we know the value of the highest and lowest points of the sinusoidal function?

Answer 4

Whatever numerical number “A” is determines our highest and lowest points

Question 5

When referring to the sinusoidal function formula, what does “d” stand for and what does it do to the function?

Answer 5

“D” signifies the vertical shift of the function. Depending on its value, the function will either shift up or down.

Question 6

How do we know if a sinusoidal function should be shifted up or down?

Answer 6

If D > 0, we shift the function up. If D < 0, we shift the function down.

Question 7

How do we know when to shift the sinusoidal function left or right?

Answer 7

How do we know when to shift the sinusoidal function left or right?

Question 8

When referring to the sinusoidal function formula, what does “c” stand for and what does it do to the function?

Answer 8

“C” signifies the horizontal shift of the function. Depending on its value, the graph will either shift left or right

Question 9

What is the formula to find a period?

Answer 9

2pi/k

Question 9

When referring to the sinusoidal function formula, what does “A” stand for and what does it do to the graph?

Answer 9

“A” signifies the amplitude of the waves. Depending on its value, it will compress, stretch, and/or flip the waves vertically

Question 9

When referring the sinusoidal function formula, what does “k” stand for and what does it do to the function?

Answer 9

“K” signifies the frequency shift of the waves. Depending on its value, it will compress or stretch the waves horizontally

Question 10

What is a period?

Answer 10

A period is the shortest distance it takes a function to repeat itself

Question 11

What is the formula for a sine sinusoidal function?

Answer 11

A*sin(k(t+/-c))+/-d

Question 12

What is the formula for a cosine sinusoidal function?

Answer 12

A*cos(k(t+/-c))+/-d

Question 13

What are sinusoidal functions?

Answer 13

Smooth, repetitive, wave-shaped graphical functions

Question 13

What is the general shape of sine and cosine when graphed?

Answer 13

Waves (like sound waves)

Question 14

How often do sine and cosine repeat?

Answer 14

They repeat every 2pi

Question 15

What happens to sine and cosine with t is negative?

Answer 15

cos(-t) = cos(t)

sin(-t) = -sin(t)

Question 16

positive

Answer 16

Positive: Quadrant 1 and 2

Negative: Quadrant 3 and 4

Question 17

What is the domain and range for sine/cosine?

Answer 17

Domain = All real number

range = -1 </= t </= 1

Question 18

When is cosine positive and negative?

Answer 18

Positive: Quadrant 1 and 4

Negative: Quadrant 2 and 3

Question 19

What are the other common trig functions we use and their formulas?

Answer 19

Tan(t) = sin(t)/sin(t)

Cot(t) = cos(t)/sin(t)

Sec(t) = 1/cos(t)

Csc(t) = 1/sin(t)

Question 19

What is the Pythagorean Identity?

Answer 19

(cos(t))^2+(sin(t))^2=1

Question 20

What values do sine and cosine correspond to in a coordinate?

Answer 20

Sine = y-coordinate of P(t)

Cosine = x-coordinate of P(t)

Question 20

What is the unit circle formula?

Answer 20

x^2+y^2=1

Question 21

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

Answer 21

(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)

Question 21

Define: Reference Number

Answer 21

A reference number is the shortest distance to the x-axis from the terminal point (P(t))

Question 22

What is negative in which quadrant?

Answer 22

Quadrant 1 = no negatives, Quadrant 2 = x negative, y positive, Quadrant 3 = both negative, Quadrant 4 = x positive, y negative

Question 23

What are the three main terminal points we will see?

Answer 23

P(pi/6), P(pi/4), P(pi/3)

Question 23

What is the circumference formula?

Answer 23

2pi * r

Question 24

What is the circumference of the circle?

Answer 24

2pi

Question 25

What direction do you move in the unit circle?

Answer 25

If t is positive, you move counter clockwise; If t is negative, you move clockwise

Question 26

Define: Terminal point

Answer 26

A terminal point is the point you end up at after moving a certain distance around the circle

Question 26

What is the notation for the terminal point?

Answer 26

P(t) where t represents the distance moved

Question 27

What is the distance formula?

Answer 27

d((x1,y1), (x2,y2))=sqrt((x2-x1)^2+(y2-y1)^2)

Question 28

Define: Unit circle

Answer 28

A circle with a radius of 1 unit with the center located at the origin