1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Aleks04 [339]
3 years ago
9

What sine function represents an amplitude of 1, a period of 2π, a horizontal shift of π, and a vertical shift of −4?

Mathematics
1 answer:
Gwar [14]3 years ago
5 0
\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\
% function transformations for trigonometric functions
\begin{array}{rllll}
% left side templates
f(x)=&{{  A}}sin({{  B}}x+{{  C}})+{{  D}}
\\\\
f(x)=&{{  A}}cos({{  B}}x+{{  C}})+{{  D}}\\\\
f(x)=&{{  A}}tan({{  B}}x+{{  C}})+{{  D}}
\end{array}
\\\\
-------------------\\\\

\bf % template detailing
\bullet \textit{ stretches or shrinks}\\
\quad \textit{horizontally by amplitude } |{{  A}}|\\\\
\bullet \textit{ flips it upside-down if }{{  A}}\textit{ is negative}\\\\
\bullet \textit{ horizontal shift by }\frac{{{  C}}}{{{  B}}}\\
\left. \qquad  \right.  if\ \frac{{{  C}}}{{{  B}}}\textit{ is negative, to the right}\\\\
\left. \qquad  \right. if\ \frac{{{  C}}}{{{  B}}}\textit{ is positive, to the left}\\\\

\bf \bullet \textit{vertical shift by }{{  D}}\\
\left. \qquad  \right. if\ {{  D}}\textit{ is negative, downwards}\\\\
\left. \qquad  \right. if\ {{  D}}\textit{ is positive, upwards}\\\\
\bullet \textit{function period or frequency}\\
\left. \qquad  \right. \frac{2\pi }{{{  B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\
\left. \qquad  \right. \frac{\pi }{{{  B}}}\ for\ tan(\theta),\ cot(\theta)

with that template in mind, let's see

the period of 2π, well, for that, you have to do nothing, because that's sine original period

Amplitude of 1, well, that's also sine's original amplitude

horizontal shift/phase... ok, that means C/B = π, now, it doesn't say if to the left or the right, so I gather either is ok, so...let's do the right

you could use then, C = -π and B = 1, that gives you -π/1 or -π

vertical shift of -4, well, that simply means D = -4

f(θ) = sin(θ - π) - 4   <-- will do
You might be interested in
Find the degree of the monomial. 4x^7y^3 a. 3 b. 10 c. 7 d. 4
Mashcka [7]
The degree of a monomial is the sum of its exponents
4x^7y^3
exponents are 7 and 3
degree is : 7 + 3 = 10
7 0
3 years ago
How many square centimeters are in an area of 5.60 in2?
Phantasy [73]

1 square inch = 2.54^2 = 6.4516 square cms

So 5.60 in^2  = 6.60 * 6.4516 =   36.13cm^2 to nearest hundredth

7 0
3 years ago
Show the expression as the base to one power. 4^5⋅4^3
White raven [17]
Hey there! :D

When you multiply powers, you add them.

You would only need to add 5 and 3 together. 

5+3= 8

4^8 <=== the answer

I hope this helps! 
~kaikers 
5 0
3 years ago
For this linear equation, give the number by which you would multiply the terms in each equation in order to eliminate one of th
Leya [2.2K]

Answer:

Step-by-step explanation:

The solution to this system of linear equations 3x – 2y = 14 and 5x + y = 32 is (x, y) is (6, 2).

6 0
2 years ago
Read 2 more answers
Find the greatest common factor of 30 and 105.
Amanda [17]
15 because it can go in to 30 to equal 2 and 105 to equal 7
8 0
3 years ago
Read 2 more answers
Other questions:
  • 91 more than the square of a number
    11·2 answers
  • Julia drinks 16 cups of water per day. How many quart(s) of water does she drink per day?
    9·2 answers
  • What is 247x56 equal
    6·2 answers
  • Tyrone saved 24$ of the 60 that he earned mowing lawns .what percent of his earnings did tyrone save
    11·1 answer
  • Your friend just purchased a new sports car for 32,000 dollars. He received 6,000 dollars for his trade in and he used that mone
    11·1 answer
  • How to do this in a 6th grade way
    15·1 answer
  • Determine whether the statement is true or false. If it is false, rewrite it as a true statement. Data at the ratio level cannot
    12·1 answer
  • The first one is done and the options for number four are:
    11·1 answer
  • Why would a bank want to loan someone money?
    14·2 answers
  • Circle the value that is not equivalent to the other values<br> 4.07 4.070 4.70 4.0700
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!