MHB What Is the Domain and Range of y=cos(3(x - 45°)) +2?

AI Thread Summary
The domain of the function y = cos(3(x - 45°)) + 2 for one cycle is determined by the interval on the x-axis where the function is defined, specifically from -45° to 90°. The range of the function is derived from the cosine function, which oscillates between -1 and 1, resulting in a vertical shift that adjusts the range to 1 to 3 after adding 2. To find these values, it is suggested to graph the function for better visualization. Understanding the definitions of domain and range is crucial for solving such problems effectively. This discussion emphasizes the importance of clarity in mathematical definitions and graphical representation.
mathuravasant
Messages
10
Reaction score
0
State the domain and range for one cycle of y=cos(3(x - 45°)) +2 Show your work.
 
Mathematics news on Phys.org
Beer induced request follows.
mathuravasant said:
State the domain and range for one cycle of y=cos(3(x - 45°)) +2 Show your work.
Please show us what you have tried and exactly where you are stuck.
We can't help you if we don't where you are stuck.
 
like how do you find domain and range off from that given equation I just don't know what to do
 
mathuravasant said:
like how do you find domain and range off from that given equation I just don't know what to do
You are having a great deal of trouble with these. I suspect the biggest cause isn't in the problems but in the definitions. I would suggest having a 3 x 5 card (or some other modern equivalent) stating what the domain, range, frequency, wave number, horizontal shift (or phase), and vertical shift are for each.

[math]y = cos( 3(x - 45) ) + 2[/math].

What is the domain? It's the interval on the x-axis that the function is defined on. So one cycle is 360 degrees. Thus
[math]0 \leq 3(x - 45) \leq 360[/math]
So what are the possible values for x? [math]0 \leq 3(x - 45)[/math] to [math]3(x - 45) \leq 360[/math]

What is the range? It's the interval on the y-axis that the function takes on over the domain. So for the sake of argument let's say that the domain is [math]-45 \leq x \leq 90[/math]. (Mind you, it isn't.) Then what is the range of cosine? It's best to graph this one and take a look since cosine "waves" so graph [math]y = cos( 3(x - 45) ) + 2[/math] and find the biggest change in y value for [math]-45 \leq x \leq 90[/math].

Let us know how it goes.

-Dan
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

B Advice to obtain the domain of compound functions
Replies
2
Views
1K
B Cosecant function: notation for the domain and range -- Am I right?
Replies
6
Views
1K
I Transformation of Functions: How Do Domain and Range Change?
Replies
4
Views
2K
MHB What are the domain and range for the inverse function $f^{-1}$ of $f$?
Replies
2
Views
2K
MHB Find the Range of a Rational Function.
Replies
1
Views
1K
MHB Sinusoidal Functions (I for this)
Replies
9
Views
992
MHB Finding the domain of this function.
Replies
5
Views
1K
MHB What Determines the Range of a Rational Function Like f(x) = 2/(x - 3)?
Replies
2
Views
1K
MHB Find Domain & Range of 8 Mathematics Problems for CSE Exam
Replies
1
Views
2K
MHB S5.t.5 Find domain and asymptotes.
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top