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]

Learn more:

https://brainly.com/question/23159335

Related Questions

easy algebra question below first correct answer gets brainliest, if you put a link i will report and block

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Answer:

6x²

Step-by-step explanation:

3x×2x=6...... then an x²

Therefore answer is 6x²

Picture included write in the simplest form

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Is "three less than a number" equivalent to "the difference of three and a number?"
Explain your answer.

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I’ll use “x” as “a number”

So it’s basically asking if-

X-3=X-3

Obviously the answer is yes.
X-3 is equal to X-3.

SOMEONE PLS HELP ME FIND THE AREA OF THIS COMPOSITE FIGURE. ILL GIVE BRAINLIEST!

Answers

For this composite question you will need to divide the shape into two different shapes. The large rectangle is going to be 60 in square because of base times height and then you would need to find the square which would be 4 times 4 cause of base times height but because it’s a triable you divide by 3 so 16/2 would be 8 than you would add both shapes and get 68 in squared. Hope that helps!

A rectangular napkin has an area of 88 square centimeters and a length of 8 centimeters.

What is the width of the napkin?

Answers

11 centimeters
This is because a rectangle has an area of length times width and so you can divide 88 by 8 to get 11

Answer:

11 cm

Step-by-step explanation:

a= l x w

88= l x 8

88/8= 11

so ll cm is the width of the napkin

4y - 18 = 20
Y=
PLEASE HELP!!!!!!!

Answers

Answer:

y = 9.5 or 19/2

Step-by-step explanation:

4y - 18 = 20

Add 18 to both sides.

4y = 38

Divide by 4.

y = 9.5 or 19/2

Answer:

34

Step-by-step explanation:

4y-18=20

+18 +18

________

4y=38

/4

________

9.5

Which line has the steepest graph?

Answers

Answer:

I think it is the fourth one

[tex]y = \frac{1}{8} x + 9[/tex]

Step-by-step explanation:

I hope that is useful for you :)

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Answers

Answer:

69824.21

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Step-by-step explanation:

Some of answers use 3,14 as a substitute for pi.
Some use the symbol for pi. which type of answers
more accurate? The more accurate value is
is

Answers

Personally i think that if you use the pi symbol it would be more accurate because on a calculator there is an pi symbol √ which is the same it will give you an answer closer to an whole number.

Find the area of the figure.

40.8 cm2

1128 cm2

47.52 cm2

33.7 cm2

Answers

Answer:

answer is 47.52 cm2

Step-by-step explanation:

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If x = 2, y = 3 and z = 5, calculate the following: 2yz ÷ 3

Answers

Step-by-step explanation:

2x 3x5 = 30 ÷ 3 = 10

hope this helps

HELP ASAPPP! I WILL GIVE BRAINLEST TO THE RIGHT PERSON

Answers

Answer:

E and H are the correct answers

Step-by-step explanation:

Please Help Me!! Will Give Brainliest!!!

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x = 2 y = 1
y = 5 x= 4
x = -2 y = -7
y= 0 x= -3

In December, a car salesman sold 60 cars. In January, he only sold 24. Find the percent decrease in his monthly sales.

Answers

Answer:   45.6

Step-by-step explanation:

60 - (24% × 60) =

60 - 24% × 60 =

(1 - 24%) × 60 =

(100% - 24%) × 60 =

76% × 60 =

76 ÷ 100 × 60 =

76 × 60 ÷ 100 =

4,560 ÷ 100 = 45.6

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Answers

Answer:

the answer is B - 96 trust me

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Answers

Answer:

See below

Step-by-step explanation:

Parallel lines have the same slope.

13) The slope would still be 2/3

14) The slope would still be 9/5

HELP ASAP!!!
Two random samples were taken to determine how often people in a community listen to the local radio station each month.

The first sample surveyed 15 people as they exited the bank on Main Street. The first sample found that the mean number of hours they listened to the radio each month was 20.

The second sample surveyed every sixth person as they exited the only local grocery store until 100 people were surveyed. The second sample found that the mean number of hours they listened to the radio each month was 12.

Which statements are true? Check all that apply.
The second sample is random.
The second sample is likely to be more representative of the population.
The first sample is likely to be more representative of the population.
The second sample will give a better representation because is it larger.
The first sample will give a better representation because it is smaller.
Community members are more likely to listen to the radio station an average of 12 hours a month than 20 hours a month.

Answers

Answer:

The answers to this question are 1,2,4,6. Hope this helps you

Step-by-step explanation:

please please do a step by step of how to solve the equation and the answer! please and thank you!

Answers

Answer:

Value of x using quadratic formula (x = -4) and (x = -5)

Step-by-step explanation:

Given:

Equation

x² + 9x + 20 = 0

Find:

Value of x using quadratic formula

Computation:

Quadratic formula = [-b±√b²-4ac] / 2a

Given equation;

x² + 9x + 20 = 0

a = 1 , b = 9 , c = 20

By putting value

[-9±√9²-4(1)(20)] / 2(1)

[-9±√81-80] / 2

[-9±√1] / 2

(-9 + 1) / 2 , (-9 - 1) / 2

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Tran is using a coordinate plane to design a treasure hunt for his students. The hunt begins at the flagpole at the origin. The first clue is hidden 5 units north of the flagpole. The second clue is located 6 units east of the flagpole. The final clue is located 5 units south of the flagpole. Plot the locations of the flagpole and the 3 clues on the coordinate plane and show the path students will follow from the flagpole to all three clues. . Each unit represents 50 feet. What is the shortest combined distance along the path from the flagpole to Clue 1 to Clue 2 and to Clue 3?

Answers

Answer:

The shortest combined distance along the path from the flagpole to Clue 1 to Clue 2 and to Clue 3 is approximately 1,031.025 feet

Step-by-step explanation:

The given coordinates of the clues for the treasure hunt are

The location of the first clue = 5 units north of the flag pole

The coordinates is (0, 5)

The location of the second clue = 6 units east of the flag pole

The coordinates is (6, 0)

The location of the final clue = 5 units south of the flag pole

The coordinates is (0, -5)

The flagpole is at the origin

The coordinates of the flagpole is (0, 0)

Each unit on the graph = 50 feet

From the drawing of the treasure hunt created with Microsoft Excel, the shortest distances between the clues are as follows;

The shortest distance between 2 points is a straight line

Therefore

The shortest length from the flagpole to Clue 1 = 5 - 0 = 5 units

The actual distance from the flagpole to Clue 1 = 5 units × 50 feet/unit = 250 feet

The length from Clue 1 to Clue 2= √(6² + 5²) = √(61) units

The actual distance from Clue 1 to Clue 2 = √(61) units × 50 feet/unit = 50·√61 feet

By similarity, the actual distance from Clue 2 to Clue 3 = 50·√61

The combined shortest distance along the path from the flagpole to Clue 1 to Clue 2 and to Clue 3 = (250 + 50·√61 + 50·√61) feet ≈ 1,031.025 feet

Plsss help I’m super stuck on this

Answers

Answer:

its  b

Step-by-step explanation:

took the quiz

Answer:

I would go with D

Step-by-step explanation:

You can look at the graph and answer it

Solve each system of equations by graphing.
y = 2x
y = x + 1

Answers

Step-by-step explanation:

The system of linear equations are , (i) y = 2x and (ii) y = x + 1 . We will find some coordinates and then we will plot its graph. The point where both Graphs will meet will be the solution of the graph .

• Finding coordinates of Equⁿ (i) :-

Step 1 : Put x = 0 :-

[tex]\tt y = 2x = 2(0) = \red{0}[/tex]

Step 2: Put x = 1 :-

[tex]\tt y = 2x = 2(1) = \red{2}[/tex]

[tex]\boxed{\begin{array}{c|c|c} \bf x & \tt 0 &\tt 1 \\ \bf y &\tt 0 & \tt 2 \end{array}}[/tex]

_________________________________

• Finding coordinates of equⁿ (ii) :-

Step 1 : Put x = 0 :-

[tex]\tt y = x + 1 = 1 + 0 = \red{1}[/tex]

Step 2: Put x = 1 :-

[tex]\tt y = x + 1 = 1 + 1 = \red{2}[/tex]

[tex]\boxed{\begin{array}{c|c|c} \bf x & \tt 0 &\tt 1 \\ \bf y &\tt 1 & \tt 2\end{array}}[/tex]

Now plot these points on the graph Taking appropriate scale . Refer to the attachment in graph . From graph the Solution is (1,2) .

F(x)=400-4/5x find the function and intercepts

Answers

Answer:

The x-intercept is (500, 0);  the y-intercept is (0, 400).

Step-by-step explanation:

F(x)=400-4/5x is already a function:  a function of x.

To find the y-intercept, set x = 0 and calculate F(0):

    F(0) = 400 - 0 = 400; the y-intercept is (0, 400).

To find the x-intercept, set F(x) = y = 0 and solve for x:

     0 = F(x) = 400 - (4/5)x, or (4/5)x = 400.  To isolate x, multiply both

     sides by (5/4):  x = (5/4)(400) = 500.  The x-intercept is (500, 0).

I need help ASAP!

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Answers

1) x axis is the line on the bottom (horizontal line)
2) y axis is the line that goes vertically
3) origin is (0,0)
4) A is the dot that is height is the middle. B is the highest dot. C is the lowest dot
5) (4,6)
6) (2,9)
7) (0,4)
8) the correct ordered pair is (7,3) because it is (x,y) and allie switched between the two

1. The X axis is the line going left and right

2. The Y axis is the line going up and down

3. The origin is the point where the X and Y axis meet; (0,0); by the 0

4. The points will be written as A, B, C. This is going from left to right. So the first box on the coordinate plane furthest to the left with be labeled with A. Then the second box furthest from the left; the middle box; will be labeled with B. Then the last box will be labeled C

5. (4,6)

6. (2,9)

7. (0,4)

8. When Allie identified the point, she mixed the X and Y coordinates. To identify a point you first want to find the point following the X axis. Then do the same with the Y axis. After doing this you should have 2 numbers, in which are 3 and 7. Now when writing the coordinates, the X axis ALWAYS comes first. So it should look like (7,3)

which set of side lengths will form a right triangle 8,15,17
7,24,26
6,8,11
10,24,25

Answers

Let’s try the pythagorean formula.

1) 8^2+15^2=17^2
289=289 Yes

2) 7^2+24^2=26^2
625 ≠ 676 No

3) 6^2+8^2=11^2
100 ≠ 121 No

4) 10^2+24^2=25^2
676 ≠ 625 No

Therefor, 8,15,17 is your answer

Enter the correct answer in the box.
Solve this system of equations.

y=2x-5
y=-2x+3


x=
y=

Answers

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

2, -1

Step-by-step explanation:

In a population of adults the proportions of people in various marital status are: Single:35%, Married: 60%, Divorced: 5%. A person is selected at random. If that person is not divorced find the probability that he or she is single.

Answers

Answer:

7/20 0r 0.35

Step-by-step explanation:

Probability of been single = percentage of single adult / sum of percentages

sum of percentages = 35 + 60 + 5 = 100

35/100 = 7/20 or 0.35


(a) Calculate 8% of £3.25.

Answers

Answer:

8÷100×3.25

=£0.26

hope it is helpful to you

Step-by-step explanation:

8÷100×3.25

=0.26

espero ter te ajudado

can someone help i dont know any of these formulas

Answers

s.a=C.A xH

v of n.o.2 =lxwxh

Step-by-step explanation:

v of no.3=πr2h and s.a=πdh

no.1=area of cross section x area of all faces and v=area of cross section x length

try those ones

Hello Kitty has created a new system of conversion for the residents of Kitty Nation. The standard for measurement of length in Kitty Nation is that 8 lenthii = 30 inches and 4 gianthii = 478.8 lenthii. If a design to be sent to Kitty Nation is 294.3 feet long, how many gianthii long will it be? (Include units)

Answers

Answer:

yvcwඨ්‍ය්වුය්tubcccccccccccccuuuuuu,,,v ttttttttrhhhhhhhhh

the CN Tower of Toronto, Canada is 553 M tall. how tall is the tower in cm

Answers

Answer:

The answer is 55,300.

Step-by-step explanation:

There are 100 centimeters in one meter so you can multiply by 100 to get the answer. I hope this helps! Have a great rest of your day!

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