Question

CAN SOMEONE PLEASEE HELP EXPLAIN TO ME..'

How can a trigonometric function be chosen to model periodic phenomena with specified amplitude, frequency, and midline?

Answer 1

@Preetha @paki @study100 @Savannahrj @samantha_honey55 @Sacraficial_smh @Orion1213 @witthan1

Answer 2

I am guessing you know how a sine wave looks like. Measuring from time = 0, the curve starts from 0, goes up, then down, and goes back up to the center line at time = 2π. It then repeats itself from then on. The length of time for one pattern (2π) is called the period, the horizontal center line is called the midline, and the amplitude is the height of the crest. Note the cosine function starts at the crest and has the same curve as the sine wave. Also note that the period of tangent is π not 2π.

-How can a trigonometric function be chosen to model periodic phenomena with specified amplitude, frequency, and midline?

Most phenomena that repeat themselves are described by a trigonometric function such as a motor, a fan, a food mixer in the kitchen, etc. Note that it is not scaled by x and y; instead it is scaled by amplitude (strength) and period (time). Which trigonometric function to choose really depends on what you are modeling; you would choose the one that's most convenient.

-How does replacing f(x) with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative) effect the graph?

f(x) + k shifts the graph up by k
k(f(x) expands the graph by k times
f(kx) shrinks the period by 1/k times
f(x + k) shifts the graph to the left by k
* Note if the k is negative it becomes the reverse.
* Note also these rules apply to all functions, not just trigonometric functions.

-How does a function model the relationship between two quantities?

Imagine a spot on an automobile tire. As the car moves the spot will go up and down. The height of the spot will be the amplitude, and the distance the tire traveled is multiple of time (period).

-What is the rate of change of a function over a specified interval?

Interestingly the rate of change of sinusoidal function is also sinusoidal, the same as the original function even though the phase is shifted.

-How can a function fitted to data be used to solve problems?

You would have to measure the amplitude (strength, height, etc.) of a repeating system and measure the time it takes to change (period).

Here is an excellent website that explains trigonometric functions.
http://www.purplemath.com/modules/grphtr...

Answer 3

I got this off of
https://answers.yahoo.com/question/index?qid=20140401182317AAvEUdB

Answer 4

@Here_to_Help15 yeah i saw that but it didnt really explain

Answer 5

well than let me see if i can explain:P

Answer 6

okay thank you

Answer 7

You need this part correct

-How can a trigonometric function be chosen to model periodic phenomena with specified amplitude, frequency, and midline?

Most phenomena that repeat themselves are described by a trigonometric function such as a motor, a fan, a food mixer in the kitchen, etc. Note that it is not scaled by x and y; instead it is scaled by amplitude (strength) and period (time). Which trigonometric function to choose really depends on what you are modeling; you would choose the one that's most convenient.

-How does replacing f(x) with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative) effect the graph?

f(x) + k shifts the graph up by k
k(f(x) expands the graph by k times
f(kx) shrinks the period by 1/k times
f(x + k) shifts the graph to the left by k
* Note if the k is negative it becomes the reverse.
* Note also these rules apply to all functions, not just trigonometric functions.

Answer 8

yes @Here_to_Help15

Answer 9

i meant this part : P


-How can a trigonometric function be chosen to model periodic phenomena with specified amplitude, frequency, and midline?

Most phenomena that repeat themselves are described by a trigonometric function such as a motor, a fan, a food mixer in the kitchen, etc. Note that it is not scaled by x and y; instead it is scaled by amplitude (strength) and period (time). Which trigonometric function to choose really depends on what you are modeling; you would choose the one that's most convenient.

Answer 10

yes that part , n its okay

Answer 11

U got it?

Answer 12

i see that but my teacher said it's not explaining the question

Answer 13

can you help me please @UnkleRhaukus @dan815

Answer 14

@IvanG @ibejacob @Oceans @Purplerainbowcherry @paki @Whitemonsterbunny17 @annas can u help with How can a trigonometric function be chosen to model periodic phenomena with specified amplitude, frequency, and midline?

Answer 15

Trigonometric functions specially the sine and cosine functions used to model oscillations... mostly in waves... as well as in harmonics... pendulums... those systems with periodical repetitions...

Answer 16

okay thank you, so can you give me an idea of how to start the paragraph @Orion1213

Answer 17

Amplitude refers to the maximum magnitude of the quantity you want to expressed...

Answer 18

Frequency is the number of repetition per second of a full wave of the function... this also represents the time period a complete wave will exist by getting its reciprocal that is \[Time=\frac{1}{Frequency}\]

Answer 19

so i could say trigonometric functions are graphed to show the period, midline, and amplitude from frequency?? @Orion1213 im confused on how to word it

Answer 20

no it only shows the behavior of the system or signal you want to represent...

Answer 21

so trigonometric functions are graphed to show the period, midline, and amplitude from the behavior of the systems?? @Orion1213

Answer 22

frequency just tell us the periodic repetitions of the quantity we are interpreting...

Answer 23

yup... you can use the word "systems"

Answer 24

so i can say trigonometric functions are graphed to show the period, midline, and amplitude from the behavior of the systems?? ... that's it?

Answer 25

yup...

Answer 26

okay thanks @Orion1213 , can you help with last one?

Answer 27

ok as long as i know it...

Answer 28

• How can the unit circle and radian measures be used to apply trigonometric functions to all real numbers?’

Answer 29

Unit circle is the basis of all values of trigonometric functions as well as the radian measurements... a complete circle measures \(2 \pi\) radians...

Answer 30

all the radians measured can be obtained 1/4 of a unit circle...

Answer 31

so to answer the question... i could say the unit circle and radian measurements can be used to apply trig functions to all real number because all the radians measured can be obtained 1/4 of a unit circle...???