if the sine ratio is given, then how can sin 0/2 be determined?

Answers

Answer 1

Step-by-step explanation:

If you know, the sine. You must find the cos ratio, using the Pythagorean trig theorem.

Next, you use the half angle identity for sin

[tex] \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos(a) }{2} } [/tex]

Example.

[tex] \sin( \alpha ) = \frac{ \sqrt{3} }{2} [/tex]

We must find

[tex] \sin( \frac{ \alpha }{2} ) [/tex]

First, use the Pythagorean identity

[tex] \sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) = 1[/tex]

[tex]( \frac{ \sqrt{3} }{2} ) {}^{2} + \cos {}^{2} (a) = 1[/tex]

[tex] \frac{3}{4} + \cos {}^{2} (a) = 1[/tex]

[tex] \cos {}^{2} (a) = \frac{1}{4} [/tex]

[tex] \cos( \alpha ) = \frac{1}{2} [/tex]

Now use the half angle identiy

[tex] \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos( \alpha ) }{2} } [/tex]

[tex] = \frac{ \sqrt{1 - \frac{1}{2} } }{ \sqrt{2} } [/tex]

[tex] = \frac{ \sqrt{ \frac{1}{2} } }{ \sqrt{2} } [/tex]

[tex] = \frac{ \sqrt{ \frac{1}{2} } }{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{ \sqrt{1} }{ \sqrt{4} } = \frac{1}{2} [/tex]

So the answer for our example is 1/2


Related Questions

There are 18 students on the debate club. How many ways can the club send 4 students to the next debate?.

Answers

Let's consider first what equation we must use:

 ⇒ use Combination Formula ⇒ [tex]._{n} C_{r}=\frac{n!}{r!(n-r)!}[/tex]

      ⇒ where 'n'  is the total number of items and 'r'

      is the number of items to choose

Let's look at the problem:

total number of students: 18number of students needed for debate: 4

Let's plug it in:

 [tex]\frac{18!}{4!*(18-4)!} =\frac{18!}{4!*14!} =\frac{18*17*16*15}{4*3*2*1} =18*17*2*5=3060[/tex]

Thus there are 3060 ways

Answer: 3060 ways

Hope that helps!

what is 14 divided bye 3

Answers

Answer:

4.66

14÷ 3 = 4 r 2

add 0 to 2 ( this attracts a decimal point in your answer)

20 ÷ 3 = 6r 2

and = 4.66

Answer: 4.66666667

Yea, no need to explain for that.

HELP ME PLEASE............................................................

Answers

Answer:

2√6

Step-by-step explanation:

find the hypotenuse of the triangle thats 3 and 7

pythagorean

3 squared + 7 squared

16 + 49 = 57

√57 is the hypotenuse

√57 is also the base of the triangle that has side thats 9

pythagorean theorem

x squared + √57 squared = 9 squared

x^2 + 57 = 81

x^2 = 81 - 57

x^2 = 24

x = √24

x = √4 * √6

x = 2√6


Find the quotient of 1 4/5 and 1 1/5
Give your answer as a fraction in its simplest form

Answers

Answer: 1 1/2

Step-by-step explanation:

1 4/5 = 9/5

1 1/5 = 6/5

[tex]\frac{9}{5} / \frac{6}{5}\\ \\\frac{9}{5} * \frac{5}{6}\\ \\\frac{45}{30} \\ \\1\frac{1}{2}[/tex]

Does this graph represent a function? Why or why not?
10-
8-
6-
2
--8-
-10-
O A. No, because it fails the vertical line test.
OB. Yes, because it passes the vertical line test.
OC. Yes, because it is a curved line.
OD. No, because it is not a straight line.
-1080

Answers

The answer is 100 percent B

Math
Club
7
6
Debate
Club
15
O
Let p: a student is in the math club and q. a student is
in the debate club.
The verbal translation of p v q is:
A student is in math club
in debate club.
pvq is true for a total of
students.

Answers

The verbal translation of p v q is:

A student is in math club OR debate club

pvq is true for a total of 28 students.

Calculations and Parameters:

Given the table:

Math Club              Debate Club

7                                           15

6      

If p represents a student from the maths club

If a represents a student from the debate club

The verbal translation of p v q is:

A student is in math club OR debate club

Hence, the total number of students based on pvq is 7 + 6 + 15= 28 students.

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In a class there are two girls for every three boys. The ratio 2 : 3 compares the
number of girls to the number of boys.
a) What is the ratio of boys to the whole class? - 3:5
b) If this class has eight girls, determine how many boys there are using the ratio that there are two girls for every three boys

Answers

Answer:

a. I'm not sure if there's more to the question but I can't answer without knowing how many is the whole class

B. 12 boys

how many minutes does the white vacuum need to clean 86.25 square feet?
black vacuum cleans 8 square feet per min

white vacuum cleans 60 square feet for 8 min

red vacuum cleans 150 square feet for 25 min

Answers

Answer:

1.5 hours

As a general rule, 1,000 square feet of the house should take 1.5 hours to clean, according to Cleaning 4 Profit. So a 3,000 square feet home should take 3 hours to clean, and so on.


An 80-centimeter ramp connects the sidewalk to the bed of a truck. If the ramp
forms a 30-degree angle with the ground, the truck bed is centimeters off the ground.

Answers

The truck bed is 40cm .

What is a right-angled triangle?

A right-angled triangle is a triangle with one of its angle 90°.

Analysis:

The ramp, the height of the truck bed from ground and the distance of truck bed to the point the ramp makes contact with the ground form a right angle triangle.

So that sin 30 = height of truck bed above ground/length of ramp

sin 30 = height/80

height of the truck = 0.5 x 80 = 40cm

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What type of function is represented by the table of values below?
y
4
8
12
16
20
A. exponential
B. cubic
C. linear
D. quadratic
X12345
X

Answers

Answer

The type of function that is represented by the table of values below is C. linear

At each point (x, y) on a graph of function f, the graph has a slope equal to 4x - 4. If the
graph of f goes through the point (2, 3), then f(x) =
A)
2x² - 4x - 4
B)
2x² - 4x
C)
2x² - 1
D)
2x² - 4x + 3
E)
16x - 12

Answers

Answer:

f(x)= 2x² - 4x + 3

Step-by-step explanation:

dy/dx = 4x - 4

y = integrate dy/dx

y = 4x²/2 - 4x + c

y = 2x² - 4x + c

at (2,3)

3 = 2(2)² - 4(2) + c

3 = 8 -8 + c

c = 3

therefore f(x)= y = 2x² - 4x + 3

The graph of the function is given by f ( x ) = 2x² - 4x + 3

What is a function rule?

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

At each point (x, y) on a graph of function f, the graph has a slope equal to 4x - 4

So , dy/dx = 4x - 4

On integrating , we get

f ( x ) = 2x² - 4x + c

where the function passes through P ( 2 , 3 )

So , 3 = 2 ( 2 )² - 4 ( 2 ) + c

c = 3

Hence , the function is f ( x ) = 2x² - 4x + 3

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help me out bro please give me the right answer

Answers

I think the answer is “always”

Answer:

Always

Step-by-step explanation:

The alternate interiors are the orange pair and the green pair in between lines a and b. They've got symmetry! Rotating one of those lines 180 degrees won't change the picture or the angles of intersection, but it will flip one onto the other. Anyway, there's you answer above, if that's all you're looking for.

Here is the graph of a quadratic function f.

Answers

Answer:

B) x² - 8x + 12

E) (x -4)² - 4

F) (x - 2)(x - 6)

Explanation:

As the graph opens upwards. The value of x² will be positive.

The x intercepts are (2, 0), (6, 0) determining (x -2)(x-6)

The (x - 4)² - 4 determines the vertex of x = 4, y = -4

When simplified:

⇒ (x -2)(x-6)

⇒ x² - 2x -6x + 12

x² - 8x + 12

You conduct a survey that asks 271 students in your class whether they are attending the class field trip. One hundred twenty-one males respond, 92 of which are attending the field trip. Thirty-one females are not attending the field trip. What percent of females are attending the class field trip?​

Answers

Answer:

79% of females are attending the class field trip

Step-by-step explanation:

Question Breakdown:

- Survey 271 students

- 121 males respond, 92 attending field trip

- 31 females not attending field trip

What percent of females are attending the class field trip?​

The two-way table or the class whether they are attending the field trip or not is attached below,

The table tells us

• Males who are not attending : 121 - 192 = 29

• Total females who responded : 271 - 121 = 150

• Females who are attending : 250 - 31 = 119

• Total students who are attending : 91 + 119 = 211

• Total students who are not attending : 29 +31 = 60

There are a total of 150 female students and 119 of them are attending the field trip

[tex]\frac{119}{150} = 0.79 x 100 = 79%[/tex]

a sticker shaped like a rectangle has an area of 56 square centimeters. it has a width of 7 centimeters.

Answers

Step-by-step explanation:

Soln:-

Given,

Area of sticker=56 cm^2

Width of sticker=7 cm

Length of sticker=?

We know that,

Area of rectangle=l×b

or,56=l×7

or,l=56÷7

•°•l=8

Hence,the required length of the sticker is 8 cm.

After surveying students in her homeroom, katie decided to use a number cube to predict the probability that a randomly chosen student in her school planned to stay after school today for extracurricular activities. in katie’s simulation, a roll of 1 represents staying after school, while rolls of 2, 3, 4, 5, or 6 represent leaving school at the end of classes. according to katie’s model, what is the probability that three randomly chosen students will all stay after school for extracurricular activities today? startfraction 1 over 729 endfraction startfraction 1 over 216 endfraction startfraction 1 over 18 endfraction startfraction 1 over 6 endfraction

Answers

Using it's concept, it is found that the probability that three randomly chosen students will all stay after school for extracurricular activities today is of [tex]\frac{1}{216}[/tex].

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, for each student, one out of six rolls represent staying after school, hence there is a [tex]\frac{1}{6}[/tex] probability they stay after school. For the three students, the probability is given by:

[tex]p = \left(\frac{1}{6}\right)^3 = \frac{1}{216}[/tex]

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In the function f(x) = a(x + 2)(x-3)^b, a and b are both
integer constants and b is positive. If the end behavior
of the graph of y = f(x) is positive for both very large
negative values of x and very large positive values of x,
what is true about a and b?
A. a is negative, and b is even.
B. a is positive, and b is even.
C. a is negative, and b is odd.
D. a is positive, and b is odd.

Answers

Using limits, considering the end behavior of the function f(x), it is found that the correct statement is given as follows:

D. a is positive, and b is odd.

What is the end behavior of a function?

It is given by it's limits as x goes to negative and positive infinity.

In this problem, we have that, considering the end behavior:

[tex]\lim_{x \rightarrow \infty} = \infty \rightarrow ax^{b + 1} = \infty[/tex][tex]\lim_{x \rightarrow -\infty} = \infty \rightarrow ax^{b + 1} = \infty[/tex]

This will only be true if a is positive and b is odd, hence option D is correct.

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.
A grab-bag contains 20 packages worth $.70 each, 15 packages $.60 cents each, and 5 packages worth $.30 each. What is the expected value if you have to pay $.50 to pick one package at random?
about $0.53
about $0.00
about $0.60
about $0.11

Answers

The expected value if I have to pick one package given the price I would have to pay is $0.11.

What is the expected value?

The expected value is the cost you would have to pay subtracted from the total value of one package.

Total value of one package  =[ (15 x 0.60) + (5 x 0.3) + (20 x 0.7)]/ (20 + 15 + 5) = $0.61

Expected value = $0.61 - $0.50 = $0.11

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Question 1 of 10
What is the effect on the graph of f(x) = x² when it is transformed to
h(x) = x² +12?

Answers

The answer is b
Solution f(x) = x^2First compress vertically by a factor of . f(x) = x ^ 3; y(x) = 1/5 * x ^ x Then I'm going move up q(x)= 1 xi x^ * Rightarrow hex)= 1/5 x^2+1

Julia made a model of a square pyramid. She used cardboard to construct the model with the dimensions shown. It has an open bottom.

A square pyramid has a square base with side lengths of 8 centimeters, and 4 triangular sides with a height of 5 centimeters.

What is the surface area of the model?
A. 80 cm2
B. 144 cm2
C. 224 cm2
D. 320 cm2

Answers

Answer:

A.  80 cm²

Step-by-step explanation:

If a square pyramid has an open base, then the surface area is made up of the 4 congruent triangular sides only.

Area of a triangle = 1/2 × base × height

Given:

Base = 8 cmHeight = 5 cm

⇒ Area of one triangular face = 1/2 × 8 × 5

                                                 = 20 cm²

⇒ Total surface area = 4 triangular faces

                                   = 4 × 20

                                   = 80 cm²

Answer:

80 cm²

Step-by-step explanation:

I did it and I got it right

can someone do this for me please?! Just the answer pls

Answers

The time taken that the aliens on Vormir will be waiting is 6 days.

How to calculate the distance?

From the information given, the speed ia given as 0.7 and the time taken is given as 8.5. It should be noted that the formula for calculating distance will be:

Time = Speed × Distance

Time = 0.7 × 8.5

Time = 6 days approximately.

Therefore, the correct option is D.

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solve for x. x^2+12x<-11

Answers

x²+12x<-11

x²+12x+11<0

x²+12x+11=0

(x+11)(x+1)=0

x+11=0 x+1=0

x= -11 x= -1

Solution: ] -11 , -1 [

A box 10 centimeters high, 5 centimeters long, and 5 centimeters wide.Find the volume of a box with a length of 5 cm, a width of 5 cm, and a height of 10 cm.

Answers

Answer:

250 [tex]cm^{3}[/tex]

Step-by-step explanation:

First, start with the formula for the volume of a rectangular prism (aka a box):

V=length*width*height

Then, plug in your values:

V=5*5*10

V=25*10

V=250

Don't forget your units!

250 [tex]cm^{3}[/tex]

Is this relation a function? Justify your answer.

Answers

Answer:

Can't see the problem. Send a picture of it.

please solve the question and give correct answer with explanation so that i can understand it​

Answers

Answer:

Yes

Step-by-step explanation:

Let the speed of the car is c and speed of the plane is p.

We are given:

The speed of the plane is 7 times the speed of the car

p = 7c

The distance traveled is

d = 315 km

The time difference to travel this same distance is 3 hours.

We know that:d = ts, where d- distance, t- time, s - speed

Find the time for car and plane and their difference.

Cart = d/s = 315/cPlanet = d/s = 315/p = 315/(7c) = 35/cThe difference315/c - 45/c = 3

Solve it for c:

(315 - 45)/c = 3270/c = 3c = 270/3c = 90 km/h

Now find the speed of plane:

p = 7c = 7*90 = 630 km/h

As we see, Jenny is right

Would the answer for c be 21 square root of 3?

Answers

Answer:

c = 14√3 km

Step-by-step explanation:

[tex]x\sqrt{3} =42\Longrightarrow x=\frac{42}{\sqrt{3} } = \frac{42 \times \sqrt{3} }{\sqrt{3}\times \sqrt{3} }=\frac{42 \times \sqrt{3} }{3 }=14 \sqrt{3}[/tex]

Since c = x

Then

c = 14√3

atty had four times as many quarters as nickels. She had $12.60 in all. How many nickels and how many quarters did
he have?
Which of the following equations could be used to solve the problem?

n+5n=1,260
25n+100 n=1,260
On+ 5 n=12.60
O5 n+100 n=12.60

Answers

it might be number b

Solve x + 5 = 7.
OA. x = -2 and x = 12
OB. x = 2 and x = -2
C. x = 2 and x = -12
OD. x = -2 and x = -12

Answers

Answer: C

|x+5| = 7 (Spilt into 2 problems)

X+5=7
X+5=-7

Solve for x on both

x=2 and x=-12

Laura worked 8 hours today. She spent
the time in meetings, on the phone,
and the rest of the time on the computer.
Make a circle graph to show how Laura
spent her work day.

Answers

Hope this explains it a little better

Multiply. Write your answer as a fraction or as a whole or mixed number.
4/5 x 3 2/3

Answers

Answer:

1 14/15

Step-by-step explanation:

Change 3 2/3 into an improper fraction, which is 11/3. When multiplying fractions, you can multiply straight across, so 11*4= 44 and 3*5 equals 15. 44/15 as a mixed fraction is 1 14/15

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In the triangle below, what is the measure of B?A. 18B. 56C. 90D. 28 In this quotation, the first stanza has a different style from the second section. What does this suggest about whitmans overall style in the poem?. write an equation using x and y to represent the hanger. what letter exists in the spanish alphabet that does not exist in the english alphabet? 1. H 2. M 3. X 4. LL Which group faced a stricter interrogation at us immigration stations during the 1800s? chinese immigrants russian immigrants irish immigrants german immigrants Inefficient problem solvers go through the same cycle as efficient problem solvers, but with a low level of stress. Select one: True False Normally, humans think of wildfires asa negative thing. In which biome canfire suppression have a considerableimpact?A. desertB. tropical rainforestC. tundraD. grassland Which disorders can be caused by inbreeding?a) albinisma genetic disorder that causes the absence of skin pigmentb) bone fracturean injury to the bones from a fall or an accidentc) flua disease caused by a virusd) hemophiliaa genetic disorder that prevents blood from clottinge) vertigoa sensation of things spinning A local business provides career training for young adults entering the workforce directly from high school. Which economic question has the business answered byfocusing on recent high school graduates? Over the last 3 months, Janet exercised a total of 101 hours. She exercised 4 hours more during the second month than the first month. In the third month, she exercised 3 hours less than the second month.Create an equation that represents this situation, where h represents the number of hours Janet exercised during the first month. Work out the area of this circle.Take pi to be 3.142 and give your answer in 2 decimal places. help me pls Is really important V=I/R correctly expresses the relationship between voltage, current, and resistance.True or False? 28) Which of the following sets of ordered pairs does not represent a linear function?(a) {(1, 2), (3, 4), (4, 5), (6, 7)}(b) {(0, 3), (1, 5), (3, 9), (1, 13)}(c) {(2, 2), (3, 3), (4, 4), (5,5)}(d) {(1, 2), (2, 2), (3, 5), (4, 8)} If the area of the region bounded by the curve y^2 =4ax and the line x= 4a is 256/3 Sq units, using integration find the value of a, where a > 0. A quart of stain covers 100 square feet. How many quarts should you buy to stain the wheelchair ramp? (Assume you do not have to stain the bottom of the ramp.) What is the name of this structural formula? Whats the answer????? #346 points!!! Which of the following is the best example of a parent striving to use positive discipline with their child?A. A parent builds a fence around the swimming pool in the yard.B. A parent models appropriate behavior when frustrated.C. A parent tells the child they do not deserve a hug after poor behavior.D. A parent reads to the child every night before bed. please help will give brainlest