Mathematics High School

Use the first five terms of the trigonometric series to approximate the value of sin to four decimal places. Then compare
the approximation to the actual value.
a. -0.9568, -0.9659
b. -0.9649, -0.9659
C. 0.5884, 0.5878
d. -0.9609, -0.9659

Use The First Five Terms Of The Trigonometric Series To Approximate The Value Of Sin To Four Decimal

Answers

Answer 1

Quick answer, without using series: sin(4π/5) must be positive since 0 < 4π/5 < π. So C is the only possible choice.

Longer, proper answer:

The first five terms in the series expansion of sin(x) are

sin(x) ≈ x - x ³/3! + x ⁵/5! - x ⁷/7! + x ⁹/9!

Now let x = 4π/5:

sin(4π/5) ≈ 0.5884

so again the answer must be C.

Answer 2

Trigonometric series :  A mathematical series whose terms proceed by sine and cosines of integral multiples of a variable angle.

Option c is correct.

First five term of Trigonometric series of sin is shown below,

   [tex]sin x=x-\frac{x^{3}}{3!}+\frac{x^{5}}{5!}-\frac{x^{7}}{7!}+\frac{x^{9}}{9!}-......[/tex]

substitute x = [tex]\frac{4\pi }{5}[/tex]

  [tex]sin \frac{4\pi }{5}=\frac{4\pi }{5}-\frac{(\frac{4\pi }{5})^{3}}{3!}+\frac{(\frac{4\pi }{5})^{5}}{5!}-\frac{(\frac{4\pi }{5})^{7}}{7!}+\frac{(\frac{4\pi }{5})^{9}}{9!}-......[/tex]

After solving,

We get, approximation value of    [tex]sin\frac{4\pi }{5}=0.5884[/tex]

Now find , actual value

              [tex]sin\frac{4\pi }{5}=0.5878[/tex]

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Related Questions

2. Tim makes a tissue box. The area of the base is 45 square inches. The height of the box is 4 inches. What is the volume of the tissue box?​

Answers

The volume of the tissue box is 180 cubic inches.

What is the volume?

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, the area of the base is 45 square inches.

The height of the box is 4 inches.

Now, volume = 45×4

= 180 cubic inches

Therefore, the volume of the tissue box is 180 cubic inches.

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which measure of center is needed in a box plot?

Answers

Answer:

Median

Step-by-step explanation

The median is the value in the center of the data

I REALLY NEED BRAINLIEST PLZ PLZ PLZ

AHH HELP RN PLEASE

IS THIS AN EXPONENTIAL FUNCTION??

Answers

Answer:

this =2.x3

Step-by-step explan

ation:

gramwergssa

Answer:

This =2.x3

Just took this same test

Ms. Costo is shopping for a new car. The salesman tells her the price will be $18,795 before a 10% discount. Ms. Costo isn’t sure she is getting the best price, so she sends Ms. Deele to ask the price of the same car. This time the salesman tells her the price is $17,050. Who is offered the better price? What is the price of the better deal after paying the 6% sales tax?​

Answers

Answer:

Ms. Costco was offered the best price. It would be $15,900.57 after tax

Step-by-step explanation:

Ms. Costco: $18,795 x .90 =$16,915.50 x .94=$15,900.57

Ms. Deele: $17,050 x .94=$16,027

hey cutie pls help me thank you ​

Answers

Answer:

the answer is 2 I believe

I think the answer is 12

what is 2/3d -8=1/2d

Answers

Answer:

d = 48

Step-by-step explanation:

Jose graphed the amount of money paid in relation to the number of avocados bought. Which stamens best describes the unit rate for the graph below?

Answers

Answer:

[tex]c \: 5dollar \: each[/tex]

Answer:

its avocados cost $5.00 each ( its c)

Consider the system of equations 3x + y = 10 and 6x – y = 17 . What is the value of the x-coordinate of its solution?

Answers

Answer:

x = 3

Step-by-step explanation:

These are simultaneous linear equations hence, we add them because +y and -y will cancel eachother.

3x + y = 10

6x - y = 17

____________

9x        = 27

  x         = 27/9

  x         = 3

So, x- coordinate is 3

Answer: the answer should be x = 3

Step-by-step explanation:

Which of the following describes the data set 6,8,13,15,21,23,31

Answers

Answer:

what are the answer choices?

i'll edit my answer if you give them to me and i know the answer

Step-by-step explanation:

Answer:

It has two numbers per turn. The first is 2 and stays the same the whole time. The second number starts as 5, but every time it hits that number, it increases by 1.

Step-by-step:

As we already know, two starts off the turn, so every number on this turn will increase by 2 (6+2=8.)

Now, for this one, we have five, so for this turn we'll increase it by that much (8+5=13).

However, this number won't stay at 5. Instead, it will increase by 1 every time we hit this turn. Let's continue one:

Turn Two = 13+2=15

Turn 5+1 = 6 = 15+6=21

Turn Two = 21+2=23

Turn 6+1 = 7 = 23+7=31

And from there, the pattern would/will continue!

Hope this helped! <3

Source(s) used: N/A

A sales team estimates that the number of new phones it will sell is a function of the price that it sets. It estimates that if it

sets the price at x dollars, it will sell f(x) = 4,920 - 6x phones. Therefore, the company's revenue is x . (4,920 - 6x). Find

the price x that will maximize the company's revenue.

Answers

Answer:

410

Step-by-step explanation:

Revenue is given by the relation :

x . (4,920 - 6x)

F(x) = 4920x - 6x²

To obtain the price, x which maximizes revenue, we take the first derivative of the revenue function and equate to 0

F'(x) = 0

F'(x) = 4920 - 12x

4920 - 12x = 0

-12x = - 4920

x = 4920 / 12

x = 410

Price will be 410

What is the length of the arc by a central angle of 85 degrees and a radius of 8cm to the nearest tenth of a cm?

Answers

Answer:

11.86824cm

Step-by-step explanation:

Answer:

11.86824cm

Step-by-step explanation:

GUYSSS PLS HELP ME IM GONNA FAIL FRR

Answers

Answer:

x = 11

Step-by-step explanation:

180 - (82+50)

180 - 132

48

5x-7 = 48

5x = 55

x = 11

Students at a middle school are divided into 6th, 7th, and 8th grades. A random sample of 15 students from each grade is chosen.
Which sampling method best describes this scenario?

A) simple random sample
B) stratified random sample
C) systematic random sample
D) voluntary response sample

Answers

Answer:

B. Stratified random sample is the correct answer

The best sampling method that describes the scenario where students from each grade (6th, 7th, and 8th) are randomly chosen in a sample of 15 students from each grade is B) stratified random sample.

In a stratified random sample, the population is divided into distinct groups or strata based on certain characteristics, and then a random sample is taken from each stratum. In this case, the distinct groups are the different grade levels (6th, 7th, and 8th grades). By randomly selecting 15 students from each grade, we ensure representation from each grade level in the sample.

This method allows for a more accurate representation of each grade level within the sample and can provide valuable insights into the characteristics and experiences of students in each grade.

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please help with this problem?!

Answers

Answer:

umm 33 i think

Step-by-step explanation:

The answer is 120 ft

find the volume of the prism. write your answer as a decimal.​

Answers

Answer:

161.21

Step-by-step explanation:

Need math help plzzzz neddd helps no links or imma report u 20 points plzz helps

Answers

Answer:

9

Keep the value of k as 9 then multiply it with the numbers in the brackets and then arrange the like terms and see yourself.

help this is 15 points

Answers

Answer:

a) 25 ft

Step-by-step explanation:

30 divided by 6 equals 5, so multiply 5 with 5 and this gets 25 ft as the height of the flagpole

Favorite Color
red
32.86 %
blue
24.36 %
yellow
15 %
green
27.78 %
1728 students were asked to name their favorite color.
The results are shown in this circle graph.
How many students gave green as their favorite?
O A 94
OB. 480
O c. 28
D. 432
O E. 568

Answers

Answer:

I say 28

Step-by-step explanation:

because its 27 and it's almost to 28

Answer:

E. 568

Step-by-step explanation:

convert the unit. of length​

Answers

Answer:

50688

Step-by-step explanation:

thats all i got sorry if thats wrong but i hope this helps.

to classify
ons.
Classify the system of equations.
– x=2-y
1 + y = 3x + 0
Click on the correct answer.
in slope-
intersecting
y-intersects.
2
parallel
coincident

Answers

Answer:

The system of linear equations consist of parallel lines

Step-by-step explanation:

Here, we want to classify the system of linear equations

Firstly, let us write both in the standard forms

For the first;

y = 3x + 2

For the second;

y = 3x-1

The general form of a linear equation is;

y = mx + b

where m is the slope and b is the y-intercept

In both cases, m = 3 and that means the slope is the same

When two lines have same slope values, they are said to be parallel to each other

question on the picture

Answers

B) 48/73
hope this helps

Can someone pleaseeee help and if you’re correct i’ll give brainliest

Answers

Answer:

can you copy and paste it on a question its kinda blurry for me

Step-by-step explanation:

Answer:

B / The Girl

Step-by-step explanation:

.

What is the volume of a square pyramid with a base length of 4 cm and a heighi of 9 cm?

Answers

Answer:

V = 48 cm³

Step-by-step explanation:

base = 4 x 4 = 16

V = 1/3(16)(9) = 48 cm³

The ratio of boys to girls in class is 4 : 5
What fraction of the class are boys

Answers

Answer:

The ratio of boys to girls is 4:5. So let 4x be the number of boys and 5x be the number of girls. Then 4x+5x = 9x is the total number of students. Then the fraction of boys in the class is 4x/9x = 4/9.

Which expression is equivalent to 3^2 x 3^6

3^12

9^12

9^8

3^8

Answers

Answer:

[tex] {3}^{8} [/tex]

Step-by-step explanation:

1) Use product rule: x^a x^b = x^a+b.

[tex] {3}^{8} [/tex]

2) Simplify.

[tex]6561[/tex]

The answer is option D) 3⁸.

Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
m-{=2+2m
СЛАМ
O 4
O 5

Answers

5 I think it’s the a

Mr. Cantu opened an account with a deposit of $2,000.

The account earned annual simple interest.
He did not make any additional deposits or withdrawals.
At the end of 8 years, the balance of the account was $3,150.
What is the annual interest rate on this account?

A) 12.5%

B) 10%

C) 8.25%

D) D) 7.19%

Answers

I think the answer is A

PLEASE HELP ILL GIVE BR4AINLIEST]
PLEASSE SHWO WORK I GOT IT WRONG

Answers

Answer:

16%

Step-by-step explanation:

Answer:

16% you just have to guess till you get it right

85*0.16=13.60

Step-by-step explanation:

Find the measure of X from the circle below:

Answers

Answer: it looks like about 180 degrees

Step-by-step explanation:

sorry if wrong can you help me if right please

Will mark brainlist if correct and it’s due soon so please help. Use the information provided to write the standard form equation of each circle

Answers

Answer:

D;

(x + 1/2)^2 + (y- √57)^2 = 81

Step-by-step explanation:

Mathematically, the general equation of a circle is given as;

(x-a)^2 + (y-b)^2 = r^2

where (a,b) represents the circle center and r represents the radius of the circle

Thus, we have this as follows;

(a,b) = (-1/2, √57) , r = 9

Substituting these values;

(x + 1/2)^2 + (y- √57)^2 = 9^2

(x + 1/2)^2 + (y- √57)^2 = 81

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