Find the exact value using a half angle identity. Cos(-pi/8)

Answers

Answer 1

9514 1404 393

Answer:

  cos(-π/8) = (√(2+√2))/2

Step-by-step explanation:

The half-angle formula is ...

  [tex]\cos{\dfrac{\theta}{2}}=\pm\sqrt{\dfrac{1+\cos{\theta}}{2}}[/tex]

Since cosine is an even function, cos(-π/8) = cos(π/8).

For θ/2 = π/8, θ = π/4 and cos(θ) = (√2)/2. Filling in the formula, we have ...

  [tex]\cos{(-\dfrac{\pi}{8})}=\cos{\dfrac{\pi}{8}}=\sqrt{\dfrac{1+\cos{\dfrac{\pi}{4}}}{2}}=\sqrt{\dfrac{1+\dfrac{\sqrt{2}}{2}}{2}}\\\\=\sqrt{\dfrac{2+\sqrt{2}}{4}}=\boxed{\dfrac{\sqrt{2+\sqrt{2}}}{2}}[/tex]


Related Questions

find the mean of the data 5,5,8 set

Answers

Answer:

the mean is 6

Step-by-step explanation:

5+5+8= 18

then divide 18 by 3 bc there is 3 numbers and u get 6

hope this helps

I need help with this question ! if someone could also explain what the answer is, that would be awesome.

Answers

Answer:

y=3/2x+3

Step-by-step explanation:

The slope is 3/2. The slope is m. We plug 3/2 into our equation.

y=mx+b

y=(3/2)x+b

Now we have to find b.

B is 3 because that's where it crosses the y axis.

So y=3/2x+3

Solve 6 < x + 5 < 11 ​

Answers

Answer:

I think it should be 1  < x ≤ 6

Step-by-step explanation:

I need help!!!! I don’t understand this at all

Answers

Answer:

ixtjtxgixgixyixiyxyifyicjgckckhckhcjgckckhckhckhcihciyciyfiyfiyfiyfiyfiyyif

Step-by-step explanation:

ridutd6utsutsursustysysyytshfzyrsyrsyrsyrsutd

What is the solution set of the equation |2x-9| = -9

Answers

Answer:

tbh i don't kno either lol

Step-by-step explanation:

hehehe

please answer for brainlesit

Answers

Answer:

(-3, -2) that is the answer please give me brainiest

Step-by-step explanation:

What is 50x50x1x0 =?
What is 0x0 =?
What is 0/0 =?

Answers

What is 50x50x1x0 = 0

What is 0x0 = 0

What is 0/0 = it is called undefined and the expression is 00

Answer:

1. 0  2.0 3. impossible

Step-by-step explanation:

1. PEMDAS

50*50=2500

2500*1=2500 idnetification property

2500*0=0  zero property

2. 0*0 =0  zero property

3. 0 can not be a divisor. This leads to the answer being an error

HELP!!!
Find the equation of a line parallel to 2x + 2y=6 that contains the point (3,-5), Write the equation in slope-intercept

Answers

Answer:

[tex]y = -x -2[/tex]

Step-by-step explanation:

Slope-Intercept form of the line

Any given line with slope m and y-intercept b can be written as:

y=mx+b

We need to find the equation of a line parallel to

2x + 2y = 6

Dividing by 2:

x + y = 3

Solving for y:

y = -x + 3

Comparing with the slope-intercept form of the line:

m = -1

Parallel lines have the same slope, thus the required line must have a slope m = -1.

Since we have a point through which the line passes, we use the point-slope form:

y - k = m ( x - h )

Where (h,k) is the point.

The required equation of the line is:

y - (-5) = -1 (x - 3)

Operating:

y + 5 = -x + 3

Solving for y:

[tex]\boxed{y = -x -2}[/tex]









Laura had 192 dollars to begin with. She just spent b dollars. Using b, write an expression for the number of dollars she has left

Answers

Answer:

uh idkbjbss codificación

192-b I think not too sure

What is the second step in identifying grouped mean?

Answers

Answer:

B

Step-by-step explanation:

Divide the sum obtained in preceding step by total number of frequencies.

Two angles are complementary. One angle is twice as large as the other angle. What is the measure of each angle?​

Answers

Angles that are complementary end up equally 90 degrees. That means 30 degrees is one and 60 is the other because 30*2 = 60
60+30=90

four students measure their height their heights measure 184cm, 192cm, 164cm, 200cm what is the mean height of the students

Answers

Answer:

add them all up and divide by four to get the mean is to get the average if there were two numbers you add and divide by 2 but since there are for u divide by four once you have added them all up

Kyle is a secretary. She earns $12.38 per hour. She worked 42 hours last week. What is her straight time pay?​

Answers

Answer:

$519.96

Step-by-step explanation:

$12.38 × 42= $519.96

Find the sum: 2.234 + 0.01

Answers

Answer:

The sum of 2.234 and 0.01 is 2.244.

Step-by-step explanation:

The 0.01 is in the hundredths place, so just add 1 to the number in the hundredths place of 2.234, to make it 2.244.

6.333 x 10^2



HHHEEEEELLLLLLLPPPPP!

Answers

Answer:

See Below

Step-by-step explanation:

6.333 x 10^2

10^2 = 100

since there is 2 zeros, move the decimal to the right twice.

633.3

633.2
Pls mark me as brainliest

For the function h(x) = x2- 2, find the range:

If the domain is {-1, 0, 3}

Answers

Answer:

-4, -2, 4

Step-by-step explanation:

-1(2)-2

0(2)-2

3(2)-2

I hope this helped.

Brent count to 10 red cards 10 Blackhearts and 20 blue cards in a deck of cards what is the radio of red cards to other cardsj

Answers

Answer:

1/4

Step-by-step explanation:

10+10+20=40

10 of those are red cards which makes it 10/40 which is simplified to 1/4.

Answer:

10:30 (simplified- 1:3)

Step-by-step explanation:

there are 10 red cards so the first number would be 10

the other cards are black hearts and blue cards, if you add them together that is 30 cards, therefore, the answer is 10:30

It has been observed that a large percentage of professional hockey players have birthdays in the first part of the year. It has been suggested that this is due to the cut-off dates for participation in the youth leagues - those born in the earlier months are older than their peers and this advantage is amplified over the years via more opportunities to train and be coached. Of the 511 professional hockey players in a season, 159 of them were born in January, February, or March.

Requried:
a. Assume that 25% of birthdays from the general population occur in January, February, or March (these actually contain 24.7% of the days of the year). In random samples of 508 people, what is the mean number of those with a birthday in January, February, or March?
b. What is the standard deviation?
c. Now, 158 of the 508 professional hockey players were born in the first three months of the year. With respect to the mean and standard deviation found in parts (a) and (b) what is the z-score for 158?
d. If the men in the professional hockey league were randomly selected from the general population, would 158players out of 508 be an unusual number of men born in the first 3 months of the year?

e. Which of the following is an acceptable sentence to explain this situation?

1. If the men in the professional hockey league were selected randomly from the general population, this would be an unusual collection of birth dates.
2. There is good reason to believe that a significantly larger than expected proportion of professional hockey league players are born in the first three months of the year.
3.This could be a result of the random variation of birth dates within a sample. However, it would be pretty unlikely to happen by chance.
4. All of these are valid statements.

Answers

Answer:

a

[tex]\mu  =  127[/tex]

b

[tex]\sigma  =  9.76[/tex]  

c

[tex]z-score  =  3.18 [/tex]

d

Yes, 158 players out of 508 is an unusual number of men born in the first 3 months of the year because the z score of 158  is  greater than  3( Note :the probability of  z-score = 3 is  97%)

e

The correct option is  option 3

Step-by-step explanation:

From the question we are told that

   The population proportion is  p =  0.25

   The sample size is  n =  508

   

Generally the mean is  mathematically represented as  

     [tex]\mu  =  np[/tex]

=>   [tex]\mu  =  508 * 0.25[/tex]

=>   [tex]\mu  =  127[/tex]

Generally the standard deviation is mathematically represented as

     [tex]\sigma  =  \sqrt{ np (1-p)}[/tex]

=>   [tex]\sigma  =  \sqrt{ 508 * 0.25 (1-0.25)}[/tex]    

=>    [tex]\sigma  =  9.76[/tex]  

Generally the z-score of  158 is mathematically represented as

    [tex]z-score  =  \frac{158 - 127}{9.76}[/tex]

=>  [tex]z-score  =  \frac{158 - 127}{9.76}[/tex]

=>  [tex]z-score  =  3.18 [/tex]

Yes, 158 players out of 508 is an unusual number of men born in the first 3 months of the year because the z score of 158  is  greater than  3( Note :the probability of  z-score = 3 is  97%)

What this means is that the almost the whole  professional hockey league player are born in the first month which is unusual

(Simplify the equation) 3n+5+2n=5+n+6n-n​

Answers

Answer:

n=0

Step-by-step explanation:

3n+5+2n=5+n+6n-n​

move like terms together

3n+2n+5=5+n+6n-n

simplify down

5n+5=5+6n

subtract 5n from each side

5=5+n

subtract 5 from each side

0=n

can someone help me solve please.. thanks..

Answers

Answer:

see below

Step-by-step explanation:

f(0) means x=0

We use the f(x) when x<5

f(0) = 0+4 = 4

f(6) means x=6  

We use the f(x) when 5≤x<7

f(6) =8

In a genetics class, 6 students have GREEN eyes, 3 students have BLUE eyes, and 11 have HAZEL eyes. If a single student is picked at random, what is the probability that their eyes are GREEN or HAZEL?​

Answers

85%

6 students have green eyes = 6/20 = 30%

11 students have hazel eyes = 11/20 = 55%

20 = number of students

So 6/20 + 11/20 = 17/20 = 85%

Answer = 85%

17/20 is the probability that their eyes are green or Hafzel.

What is Probability?

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

The number of students having Green eyes =6

The number of students having Blue eyes =3

The number of students having Hafzel eyes =11

The total number of students=11+3+6

=20

The probability that their eyes are green is 6/20

The probability that their eyes are Hafzel is 11/20

The probability that their eyes are green or  Hafzel

6/20 + 11/20

= 17/20

Hence,  17/20 is the probability that their eyes are green or Hafzel.

To learn more on probability click:

https://brainly.com/question/11234923

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show me the venn diagram​

Answers

Step-by-step explanation:

A Venn diagram, also called primary diagram, set diagram or logic diagram, is a diagram that shows all possible logical relations between a finite collection of different sets. These diagrams depict elements as points in the plane, and sets as regions inside closed curves. A Venn diagram consists of multiple overlapping closed curves, usually circles, each representing a set. The points inside a curve labelled S represent elements of the set S, while points outside the boundary represent elements not in the set S. This lends itself to intuitive visualizations; for example, the set of all elements that are members of both sets S and T, denoted S ∩ T and read "the intersection of S and T", is represented visually by the area of overlap of the regions S and T.[1][2] In Venn diagrams, the curves are overlapped in every possible way, showing all possible relations between the sets. They are thus a special case of Euler diagrams, which do not necessarily show all relations. Venn diagrams were conceived around 1880 by John Venn. They are used to teach elementary set theory, as well as illustrate simple set relationships in probability, logic, statistics, linguistics, and computer science.

Venn diagram showing the uppercase glyphs shared by the Greek, Latin, and Cyrillic alphabets

A Venn diagram in which the area of each shape is proportional to the number of elements it contains is called an area-proportional (or scaled Venn diagram).

A researcher predicts that listening to music while solving math problems willmake a particular brain area more active. To test this, a research participant hasher brain scanned while listening to music and solving math problems, and thebrain area of interest has a percentage signal change of 58. From many previousstudies with this same math problems procedure (but not listening to music), it isknown that the signal change in this brain area is normally distributed with amean of 35 and a standard deviation of 10.
(a) Using the .01 level, what shouldthe researcher conclude? Solve this problem explicitly using all five steps of hypothesistesting, and illustrate your answer with a sketch showing the comparisondistribution, the cutoff (or cutoffs), and the score of the sample on this distribution.(b) Then explain your answer to someone who has never had a course in statistics(but who is familiar with mean, standard deviation, and Z scores).

Answers

Answer:

one equal to 5

Step-by-step explanation:

5x x 66

lines A and B are parallel,lines x and y are transversals. if angle 2 is 57 degrees and angle 3 is 85 degrees,find the measure of angle 5 will mark brainest​

Answers

Answer:

38

Step-by-step explanation:

see attached

Lil baby - It’s too many mothers that grieving they killing us for no reason been going on for too long to get even

Answers

Answer:

[tex]its \: 11.75[/tex]

Division.

35.25 divided by 3 equals 11.75.

Answer: $11.75 each hat.

(x^4 +3x^3 -2x^3)(-5x^2 +x) = (x^4 +3x^3 -2x^3)(-5x^2)+(x^4 +3x^3 -2x^3)(x) is an example of what?
a) vertical multiplication
b) FOIL
c)The Distributive Property
d) multiplying two binomials

Answers

Answer: The distributive property.

Step-by-step explanation:

(x^4 +3x^3 -2x^3)(-5x^2 +x) = (x^4 +3x^3 -2x^3)(-5x^2)+(x^4 +3x^3 -2x^3)(x) is an example of the Distributive Property.

What is the Distributive Property?

It is a property of multiplication and division. It states that when either of these operations is written outside a bracket, the operation must be applied to all terms inside the bracket when it is opened.

(a + b)c = ac + bc

The given equation is an example of:

It is given that:

(x^4 +3x^3 -2x^3)(-5x^2 +x) = (x^4 +3x^3 -2x^3)(-5x^2)+(x^4 +3x^3 -2x^3)(x).

We can see that when the bracket of the second term is opened, the first term is multiplied across all the terms that were within the bracket.

This is a feature of the distributive property. It is called the distributive property of multiplication.

Therefore, we have found that the equation (x^4 +3x^3 -2x^3)(-5x^2 +x) = (x^4 +3x^3 -2x^3)(-5x^2)+(x^4 +3x^3 -2x^3)(x) is an example of the Distributive Property.

Learn more about the Distributive Property here: https://brainly.com/question/1780105

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A package of 5 pairs of insulated socks costs ​$37.95. What is the unit price of the pairs of socks​?

Answers

Answer:

$7.59.

Step-by-step explanation:

Divide $37.95 dollars (converting it into 37.95), by 5, and you get 7.59 ($7.59).

Answer:

$7.59

Step-by-step explanation:

you dived $37.95 by 5 and you get your answer of $7.59

write a decimal number
ral for 3/5​

Answers

Answer:

0.6 or 0.60

Step-by-step explanation:

3/5 mulitply denominator to see how much it goes to 100 which is 20 so 5x20 which is 100 and u go to other number u get 60 so 60/100 or you can just divide 3 by 5 which is also 0.6

The answer is 0.6 for your problem

Evaluate and reduce:
7
3
--
8
16
Enter the number that belongs in the
green box.
[?]
Enter

Answers

Answer:

Step-by-step explanation:

7/8 + 3/16

14/16 + 3/16

17/16

It will be nice if you give me brainliest.Good luck!

There are eight wires which need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attached in any order, and the production manager wishes to determine which order would be fastest for the robot to use. Use the multiplication rule of counting to determine the number of possible sequences of assembly that must be tested.

Answers

Answer: 40320 sequence to test.

Step-by-step explanation:

we have given the following data:

No of wires which need to be attached to a circuit board = 8

What We need to find is the number of possible sequences of assembly that must be tested.

Using our multiplication rule of counting we arrive at,

Number of possible sequences of assembly is given by

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

= 40320

i.e. there are 8 choices for the first wire, 7 choices for the second wire, 6 choices for the third wire, 5 choice for the fourth wire same till the 8th wire.

Hence, there are 40320 possible sequences of assembly.

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