Hello people ~
plot the graph of y=cos x
Answers
Step-by-step explanation:
[tex]\displaystyle \boxed {y = sin\:(x + \frac{\pi}{2})} \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{2}} \hookrightarrow \frac{-\frac{\pi}{2}}{1} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 1[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 1[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = sin\:x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{2}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{2}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{2}} = \frac{-\frac{\pi}{2}}{1}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = sin\:(x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a wourd problem to wourk with, you MUST use the above formula for calculating the period. Onse you do that, the rest should be easy. Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended one unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Answer:
Properties of y = cos(x)
The cosine wave is a sinusoidal function (sine and cosine waves are the same except for a horizontal shift).
It is a continuous function and so its domain is (-∞, ∞)
The center line is y = 0
The Amplitude (the height from the center line to the peak) is 1, and so its range is -1 ≤ x ≤ 1
The y-intercept is at (0, 1)
Its period (length of one wave) is 2π (360°)
Related Questions
Which line has an undefined slope?
y = x-5
3y - 6x = 0
x= 10
y = -5
Answers
Answer:
x = 10
Step-by-step explanation:
Y = x-5 has a slope of 1
3y - 6x = 0 is a clear linear equation with a Y-intercept of 0
y = -5 has no slope
x = 10 is a line going straight up and intersects the point (10, 0)
Which is an undefined slope
Which polynomials are in standard form?
Choose all answers that apply:
(Choice A, Checked)
A
t^4-1t
4
−1t, start superscript, 4, end superscript, minus, 1
(Choice B, Checked)
B
-2t^2+3t+4−2t
2
+3t+4minus, 2, t, squared, plus, 3, t, plus, 4
(Choice C, Checked)
C
4t-74t−74, t, minus, 7
(Choice D)
D
None of the above
Answers
Answer:
a c
Step-by-step explanation:
PLEASE ANSWER (100points)
When evaluating (6 x + 9) squared minus 5 for x = 1, the given value of 1 is substituted for what part of the expression?
the exponent
the constant
the variable
any numerical value
Answers
Answer:
the variable
Step-by-step explanation:
Given expression:
[tex](6x+9)^2-5[/tex]
When evaluating the expression for [tex]x=1[/tex], we need substitute 1 for the variable ([tex]x[/tex]) in the expression.
Evaluating the expression for [tex]x=1[/tex]:
[tex]\implies (6\cdot1+9)^2-5[/tex]
[tex]\implies (6+9)^2-5[/tex]
[tex]\implies (15)^2-5[/tex]
[tex]\implies 225-5[/tex]
[tex]\implies 220[/tex]
Answer:
Variable
As variable is x and we have to substitute x=1Step-by-step explanation:
Let's find the value
[tex]\\ \rm\Rrightarrow (6x+9)^2-5[/tex]
[tex]\\ \rm\Rrightarrow (6+9)^2-5[/tex]
[tex]\\ \rm\Rrightarrow 14^2-5[/tex]
[tex]\\ \rm\Rrightarrow 196-5[/tex]
[tex]\\ \rm\Rrightarrow 191[/tex]
Congruent Triangle are?
Answers
Answer:
Triangles that have exactly the same size and shape are called congruent triangles. The symbol for congruent is ≅. Two triangles are congruent when the three sides and the three angles of one triangle have the same measurements as the three sides and three angles of another triangle.
Answer:
have exactly the same size and shape
Step-by-step explanation:
triangles are congruent when they have three sides
What would happen if I press the "Restart" button on my android phone?
Answers
Answer:
?
Step-by-step explanation:
Your phone restarts, and then boots up when u hit the on button again. you should not lose any data or anything.
please mark as brainlest.
Answer:
What would happened is all your apps will be closed and it will reboot all of your apps.It won't delete any apps.It's just like an iphone.
Step-by-step explanation:
Brainly Please
Find the distance between the points.
(5 ,10) and (negative 3 ,10)
Answers
Answer:
8 unit difference x, stays the same on y
Step-by-step explanation:
5 to -3 = 8 units
Which fruit has the lowest unit price?
A.
2.5 pounds of grapes for $4.19
B.
4 pounds of apples for $5.49
C.
5 pounds of oranges for $6.99
D.
6.5 pounds of strawberries for $9.59
Answers
Answer:
A unit is a measure of ratio between two quantities. In this instance, the unit is a pound. The ratio you need to take is the price of each fruit and divide it by the number of pounds each fruit has to get a price per pound. See below for solution.
Step-by-step explanation:
A. 4.19 dollars / 2.5 pounds = 1.676 dollars / pound
B. 5.49 dollars / 4 pounds = 1.3725 dollars / pound
C. 6.99 dollars / 5 pounds = 1.398 dollars / pound
D. 9.59 dollars / 6.5 pounds = 1.475 dollars / pound
The lowest is B, the apples.
Carla is a waitress at Daybreak Diner, and she earns $5 for each hour she works. Last week, she
out earned $148 total, including $68 in tips. How many hours did Carla work last week?
Answers
Answer:
16 hours
Step-by-step explanation:
148 - 68 = 80
80 / 5 = 16
16
Explication:
148-68=80
80➗ 5= 16
Identify the domain of the function show in the graph.
A.-1 <x <0
B.x>0
C.x is all real numbers.
D.-1 <x<1
Answers
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[tex]
x \: \: is \: \: all \: \: real \: \: numbers.[/tex]
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Thus the correct answer is (( C )) .
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Which point would not be a solution to the system of linear inequalities shown below?
Answers
Answer:
The coordinates (12,7) would NOT be a solution to the system of linear inequalities shown below.
Step-by-step explanation:
If you do the graphing and you look at all your options of coordinates, (12,7) is the only one that is not in the shaded areas or in the lines of the inequalities. Therefore, (12,7) should be the answer to that question. :)
Suppose an exponential function can be written in the form y=ab^x, and we know the common ratio b and some point (ℎ,k). True or false: The function can also be written as y=k·b^x-h.
Answers
Answer:
true
Step-by-step explanation:
y = ab^x
the coordinates of the point are x and y values.
so, we can express "a" by these values :
k = ab^h
a = k/(b^h) = k × b^-h
now we use this identity in the original equation and get
y = k × b^-h × b^x = k×b^(x-h)
and that is exactly the same as the proposed form.
Helppppp meeeeee question 2 pleaseeee !!
Answers
What is below the question is what I mean.
50 POINTS!!!
SOLVE!!!!!!!!!!!
Answers
Answer:
Range of the function is {7,5,2,0}
Step-by-step explanation:
hope it helps you
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thanks
Answer:
{7, 5, 2, 0}
Step-by-step explanation:
The domain is essentially all the [tex]x[/tex] values of the function, where the range is the value of [tex]h(x)[/tex].
So in order to solve this we simply plug in each number into the equation and get:
[tex]h(x)=|-2-5| = |-7|=7[/tex]
[tex]h(x)=|0-5| = |-5|=5[/tex]
[tex]h(x)=|3-5| = |-2|=2[/tex]
[tex]h(x)=|5-5|=|0|=0[/tex]
Therefore the range is: {7, 5, 2, 0}
Please help!!!!!! Hurry i only have 10 mins ill give brainy
Which operation should be used to solve LaTeX: \frac{x}{3} = 15x3=15 ?
Group of answer choices
+ 3
÷ 3
x 3
– 3
Answers
Carlos and Diya perform the same transformations on the same pre-image, but in reverse order.
Carlos translates, then dilates.
Diya dilates, then translates.
Carlos claims the resulting images will always be the same. Diya disagrees.
Who is right? and why
Answers
Answer:Diya
Step-by-step explanation: she’s right because she is black and all black peoples is always right
Please help (explain pls)
Answers
Answer:
C
Step-by-step explanation:
The reason it is C is mainly because it is the only line with a negative slope. A negative slope this direct \. It is not A because that is a positive slope (/). It is not B because that line is undefined which means it would look like this x = 2. And D is wrong because that is a zero slope line which looks like this y = 5. So it is C.
Here is a helpful website for problems like this Desmos. com
A train travels at a rate of (4x + 5) miles per hour. How many miles can it travel at that rate in
(x - 1) hours? Express your answer as a polynomial.
Answers
(4x+5) miles..........1 hour
x miles .........(x-1) hour
(4x+5) * (x-1) = 1 * x
in (x - 1)h = x / (4x+5) miles
Owen has a mask collection of 300 masks he keeps 63 of the masks on his wall what percentage of Owens mask collection does he keep on his wall
Answers
What do you call the point where a perpendicular bisector crosses another line?
Answers
Answer:
If AB crosses at a right angle, it is called the "perpendicular bisector" of PQ. If it crosses at any other angle it is simply called a bisector. Drag the points A or B and see both types. For obvious reasons, the point F is called the midpoint of the line PQ. See also Angle bisector.
You earn $1500 a month and 1/4 of your money goes to pay rent. What expression represents the money you have after you pay rent?
Answers
Answer:
x-375
Step-by-step explanation:
First, we find a fourth of $1500.
1/4*1500=375
Then we know that you need to pay $375. We will represent the money right before you pay as x, or any variable you choose.
= x-375
plsssss help no one is helping me
Answers
Answer:
x=-3
Step-by-step explanation:
there are three x's and five one's so the equation is 3x+5
on the other side there are 2 negative x's and 10 negative one's so the equation is -2x-10
set them equal to each other
3x+5=-2x-10
5x=-15
x=-3
Answer:
hey how old are you
Step-by-step explanation:
jnedjed
helpppppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
31
Step-by-step
161/52=can go in 3 times then you bring down the 2 then it becomes 1 because 52 /52 =1
31
1612
-156
52
-52
=0
Answer:The first error was made in step 1
The quotient should be 31
Step-by-step explanation:
f [ x ] = [ x - 3] [ x + 8 ]
Answers
Answer:
f [ x ] = [ x - 3] [ x + 8 ] = x^2 + 5x - 24
Step-by-step explanation:
f (x)=[ x - 3] [ x + 8 ]
x [ x + 8 ] -3[ x + 8 ]
x^2 + 8x - 3x - 24
x^2 + 5x - 24
if 11 is subratecet from 4 times a number the result is 89 find the number
Answers
Answer:
25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
4x-11=89
4x=89+11
4x=100
x= 25
I hope this will help
16(2x + 3) (3x + 5) ÷ 8 (2x + 3)
Answers
Answer:
2(3x+5) OR (6x+10)
Step-by-step explanation:
16 (2x+3) (3x+5)8 (2x+3)
16 (3x+5)8
2 (3x+5) = 6x+5 ThxWhich expression is a polynomial
Answers
Answer:
Second one
Step-by-step explanation:
Polynomial is when there are multiple terms
Second one is the only one that has more than one term and thus is a polynomial
What letter is located at approximately right answers only
√
22
A E
B F
C G
D H
Answers
Answer: B
Step-by-step explanation:
PLS HELP ME DUE TODAY
Answers
Answer:
Domain: (-∞, -5) (-1, ∞)
Step-by-step explanation:
Note:
For f(x) > 0: See the points of x for which the graph of f(x) lies above the x-axis.
For f(x) < 0: See the points of x for which the graph of f(x) lies below the x-axis.
We need to find the domain of f(x) for which f(x) < 0
From the graph, we can tell:
f(x) < 0 on (-∞, -5) ∪ (-1, ∞)
Therefore: The domain on which the given graph f(x) is negative, is (-∞, -5) ∪ (-1, ∞)
In a setting where a situation is described for which optimal parameters are sought, how do we develop a function that models the situation and use calculus to find the desired maximum or minimum
Answers
In order to develop a function that models the situation regarding the optimal parameters, the following are needed:
Introduce the variables.Find an equation relating to the variable.Maximize the quantity.Look that the critical points to determine the extrema.Wnat is a function?It should be noted that a function simply means the relation or expression that has to do with two or more variables.
In this case, to develop a function that models the situation regarding the optimal parameters, one has to introduce the variables and find an equation relating to the variable.
Learn more about functions on:
https://brainly.com/question/24380382
Please help with this question :)
Answers
CS = x, and since AB = BC = CD = DA = 1cm -> SD = 1 - x
We see that angle DSP = angle APQ (because they simultaneously equal to 90 when added angle DPS)
So, triangle DSP = triangle APQ (equal hypotenuse - square side and equal angle.)
Similarly, we can prove triangle SCE and QBE in the same way
So, all 4 of the triangles are equal to each other.
-> SD = CE = BQ = AP = 1-x
Calculate the area of 4 triangles : [ x(1-x) : 2 ] x 4 = x(1-x) x 2
Area (PQRS) = 1 - [ x(1-x)] x 2 = 1 - 2x + 2x(squared) = [tex]2x^{2} -2x + 1[/tex]
ii) Half area of PQRS = [tex]x^{2} -x+1[/tex]
= [tex]x^{2} -\frac{1}{2} x-\frac{1}{2} x + \frac{1}{2} = x(x-\frac{1}{2} )- \frac{1}{2}(x-\frac{1}{2} ) + \frac{1}{4} = (x-\frac{1}{2})^{2} + \frac{1}{4}[/tex]
We have : [tex](x-\frac{1}{2}) ^{2}[/tex]
has the smallest value of 0 -> The smallest half value of PQRS = 1/4 -> The smallest value of PQRS = 1/2