What is the equation of the trigonometric graph.

What Is The Equation Of The Trigonometric Graph.

Answers

Answer 1

Answer(s):

[tex]\displaystyle y = 4sin\:(x + \frac{\pi}{2}) - 1 \\ y = 4cos\:x - 1[/tex]

Explanation:

[tex]\displaystyle 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 -1 \\ 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 4[/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 -1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 4[/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 = 4sin\:x - 1,[/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 BACK [tex]\displaystyle \frac{\pi}{2}\:unit,[/tex] which means the C-term will be negative, and 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 = 4sin\:(x + \frac{\pi}{2}) - 1.[/tex] Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [0, 3],[/tex] from there to [tex]\displaystyle [2\pi, 3],[/tex] they are obviously [tex]\displaystyle 2\pi\:units[/tex] apart, telling you that the period of the graph is [tex]\displaystyle 2\pi.[/tex] 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 = -1,[/tex] in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts horisontally, the midline will ALWAYS follow.

I am delighted to assist you at any time.

What Is The Equation Of The Trigonometric Graph.
What Is The Equation Of The Trigonometric Graph.

Related Questions

Overnight, a pipe cracked and started to leak into a basementThe graph shows the depth of the water in relation to time
A.) How many inches does the water rise each hour?
B.) How deep is the water after four hours?
C.) How long will take for the water to reach a depth of 80 inches?

Answers

Answer:

Each hour the water will rise 10 in. After 4 hours the water will be 40 in deep. It will take 8 hours for the water to reach a depth of 80 in.

what is angle 1? i really appreciate the help

Answers

Answer:

53°

Step-by-step explanation:

[tex]m \angle1 = \frac{1}{2} (50 + 56) \degree \\ \\ = \frac{1}{2} \times 106 \degree \\ \\ = 53 \degree[/tex]

the ratio of men to women working for a company is 4 to 7 if there are 231 employees total how many women work for the company.

Answers

Answer:

297

Step-by-step explanation:

Ravi borrows $950 from his parents with a simple interest rate of %5. If it takes him 2 years to pay back the money, how much interest will he owe?

Answers

Answer:

he will owe $1,047 in total and $97.37 in interest

John went shopping for a pair of jeans.
The whole store was 40% off. If the
jeans John picked out were originally
$70, how much would the jeans cost with
The discount?

Answers

Answer:

it should be 42 hope it helps

Step-by-step explanation:

Determine the volume of the rectangular prism.

Answers

the volume is equal to 10/7 cm3

Answer:

30/7 x 1/3 = 1 3/7 cm^3

Help ASAP thank you!

Answers

This is D.5 units
…………….

Isaac saw a video game on sale for a 25% discount. The amount of discount is $4. What is the regular price of the video game

Answers

Answer:

The original price was $16

Step-by-step explanation:

$4= 25% of What price?

4= .25 x W

Divide both sides by .25

This leaves the equation as 16=W

Please help me I will give branliest! Find the two missing sides and write your answer as in simplified radical form. image attached

Answers

Answer:

x = y = 15[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the sine ratio and the exact value

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{30}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

2x = 30[tex]\sqrt{2}[/tex] ( divide both sides by 2 )

x = 15[tex]\sqrt{2}[/tex]

The triangle is isosceles (45- 45- 90) , then 2 legs are congruent, so

y = x = 15[tex]\sqrt{2}[/tex]

Dan used 942 units of electricity from July to October
The meter reading in July was 32 347 units.
a)
Work out the meter reading in October.
b)
Each unit costs 14p.
How much do 942 units cost?​

Answers

Answer:

13,188

Step-by-step explanation:

14 × 942

That will give you 13,188

Answer:

a) 33289

b) £131.88

Step-by-step explanation:

→ To find the meter reading add the July reading to the units used

32347 + 942 = 33289

→ Multiply the unit price by the units used

0.14 × 942 = 131.88

Some for all values of x by factoring

Answers

Answer:

{-1, 10}

Step-by-step explanation:

Next time please share the entire set of instrutions.

x^2 - 9x - 15 = -5 should be rewritten in standard quadratic form:

x^2 - 9x - 10 = 0 = (x - 10)(x + 1) = 0.

Setting each factor equal to zero and then solving for x yields {-1, 10}

Answer:

{-1,10}

Step-by-step explanation:

[tex]x^2-9x-15=-5[/tex]   given

[tex]x^2-9x-10=0[/tex]   addition property of equality

[tex]x^2+(x-10x)-10=x^2+x-10x-10=0[/tex]   x-10x = -9x

[tex]x(x+1)-10(x+1)=0[/tex]   distributive property ( x( y + z ) = xy + xz

[tex](x-10)(x+1)=0[/tex]   distributive property (backwards)

[tex]x-10=0;x=10;x+1=0;x=-1[/tex]   at least one factor of 0 has to be 0

{-1,10}

Dose anyone know how to solve this?

Answers

Hi there! We are given three functions below:

[tex] \large \boxed{f(x) = \frac{2 + {x}^{2} }{x + 6}} \\ \large \boxed{g(x) = \sqrt{1 + 7x} } \\ \large \boxed{h(x) = | \frac{3}{4} x - 14 | }[/tex]

Next, we are going to substitute the values that replace x-term. Substitute these values in each functions.

We are given below:

f(4)g(2)h(8)

Therefore,

[tex] \large{f(4) = \frac{2 + {4}^{2} }{4 + 6} } \\ \large{g(2) = \sqrt{1 + 7(2)} } \\ \large{h(8) = | \frac{3}{4} (8) - 14}| [/tex]

Then evaluate the value.

[tex] \large{f(4) = \frac{2 + 16}{10} } \\ \large{g(2) = \sqrt{1 + 14} } \\ \large{h(8) = | 3(2) - 14}| [/tex]

[tex] \large{f(4) = \frac{18}{10} \longrightarrow \frac{9}{5} } \\ \large{g(2) = \sqrt{15} } \\ \large{h(8) = | 6- 14| \longrightarrow | - 8| = 8 }[/tex]

Answer

f(4) = 9/5g(2) = sqrt(15)h(8) = 8

Which is the inverse of the difference of 1/3 - 1/4? A. 0/1
B. 1/12
C. 7/12
D.12/1
Please Help​

Answers

Answer:

12/1

Step-by-step explanation:

In the LifeSmarts event, students compete

Answers

Answer:

in pairs

Step-by-step explanation:

i just took the quiz

The inverse of y = e^x

Answers

I hope this helps!!!!

how much simple interest is accumulated if you deposit $100 in the bank at 5% interest for 15 years

Answers

Answer:

You will make 75 dollars.

Step-by-step explanation:

5% of 100 is 5. Multiply 5 by 15 to get 75.

Please help me I don't understand. If you explain it too it would really help.

Answers

Answer:

12 square feet

Step-by-step explanation:

To find the area of a triangle you have to multiply the base and height and divide it by two

6 * 4 = 24

24 / 2 = 12

Answer:

12sq.ft

Step-by-step explanation:

Area of∆=1/2x base x height

=1/2 x4 x6

=1/2 x 24

=12

MARK ME BRAINLIEST THANKS MY ANSWER PLEASE DO

Given
mZLON is a straight angle.
MZLOM = 4x + 30°
mZMON = 8x + 90°
Find mZMON:
Help pls

Answers

Step-by-step explanation:

these are supplementary angles

LOM + MON = 180

(4x + 30) + 8x + 90 = 180

12x + 120 = 180

solve for x and then substitute into 8x +90

I need help I don’t understand how I’m supposed to do this

Answers

1. The two figures are not congruent because they are not the same shape size,or length.

2.The two figures are congruent because they are the same shape,size, and length. The transformation used is reflections because they are both the same shape just flipped.


I hope I’m right and that helped

Please help !!!

A
E
B
Point
is the vertex of the angle marked in the figure.

Answers

Answer:

Point E

Step-by-step explanation:

A vertex can be described as an angle formed when two lines intersect or join together. In the figure given, point E is the intersection point.

The point that is referred to as the vertex of the marked angle where the two lines intersect is point E.

Point E is the vertex of <BEC.

help mee asappp plsssss​

Answers

multiply the area of a circle by 180/360 because you are finding the area of half a circle. if the angle of a full circle is 360, half a circle is 180

a triangle having no side congruent is called​

Answers

Answer:

A triangle without any congruent sides or angles is called a scalene triangle. When two triangles are congruent it means that they have the same size and shape.

Step-by-step explanation:

A triangle having no side congruent is called​ is called Scalene triangle.

We have a triangle having no side congruent.

We have to identify the name of this triangle.

What is a Triangle ?

A triangle is a plane figure with three straight sides and three angles.

According to question, we have -

A triangle with no side congruent. If all the three sides of a triangle are of same length then it is called congruent triangle. It is also called Equilateral triangle. Similarly, a triangle with none of its sides equal or congruent is called a Scalene triangle.

Hence, a triangle having no side congruent is called​ is called Scalene triangle.

To solve more questions on Scalene triangle , visit the link below -

https://brainly.com/question/10651823

#SPJ6

which quadrilateral has diagonals that are congruent but do not bisect each other

Answers

C. A rhombus

Hope this helps!

Please help me asap!​

Answers

Answer:

Let's analyze the example first:

We have:

3, 4, 6      target 42    answer: (3 + 4)*6

If we solve the equation, we get:

(3 + 4)*6 = 7*6 = 42

So, we need to reorder the first 3 numbers in an expression, such that the solution of the expression is the target number.

a) 2, 5, 6     Target 40

We know that 5*8 = 40

and that 2 + 6 = 8

Then the answer is:

(2 + 6)*5

b) 3, 4, 6  target 12

Here we know that 4*3 = 12

and 6 - 3 = 3

Then the answer is:

(6 - 3)*4

c) 4, 6, 10   target 1.

We know that the quotient of two equal numbers is 1.

And 4 + 6 = 10

Then the answer here is:

(4 + 6)/10

d) 3, 5, 6 target 21

We know that 3*5 = 15

And 15 + 6 = 21

Then the answer here is:

3*5 + 6

e) 2, 7, 10  target 6.

Here is a harder one.

We know that 2*3 = 6

And that 10 - 7 = 3

Then the answer ere is:

2*(10 - 7)

f) 3, 6, 15   target  3

Here we can use:

(15 - 6) = 9

And 9/3 = 3

Then the answer is:

(15 - 6)/3

Classify the triangle with side lengths of 5, 6, 7

Answers

Answer:

Scalene triangle

Step-by-step explanation:

The sides of the triangle is ,

5 , 6 , 7

Since the sides are unequal . Hence it is a scalene triangle .

Hence the ∆ is scalene triangle .

I NEED HELP! I HAVE A TEST TOMORROW AND I NEVER PAYED ATTENTION!!! Whats the variable next to the number?? Like 2c or 6y

Answers

Answer:

It means you multiply the number by that variable.

Step-by-step explanation:

This is used to shorten the equation with a variable.  For example, 2c means 2 times c.  6y means 6 times y.  

PLEASE HELP ME I AM BEING TIMED, I WILL MARK THE BRAINLIEST TO WHOEVER GETS THIS RIGHT, WITH AN EXTRA 10 POINTS!

Answers

Answer:

a)9

Step-by-step explanation:

i dont know what b is sorry

Answer: (a) = The gcf of 63 and 36 is 9. (b) = 9 x (7 - 4)

Step-by-step explanation:

please help.. don't get it

Answers

Y=26

Hope this helped

Discriminat of 3x^2+15x-6=0

Answers

Solution

=−5±33√2

jjkk,m

I've had to repost this question like 4 times because ppl put fake answers, pls put the answer if u know it and dont lie

Answers

Answer:

189.05 ft^3

Step-by-step explanation:

I think this is the right answer but I'm not 100% sure.

So first, you need to find the area of the rectangular prism. 5*5=25, and there are 5 of these rectangles (4 sides and the bottom), so the total is 125 ft^3. I don't think you would include the area of the top, as the top is not flat, and has a pyramid on it.

To find the area of the pyramid, there is a somewhat complicated and long equation that I can't write here, but you can look up the formula for the area of a square pyramid.

The area of the pyramid is around 64.05 ft^3. 125+64.05=189.0500 rounded to the nearest hundredth is 189.05 ft^3.

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