Simplify the expression 1/√(1-cos^2 x) . Remember cos x= 1/csc x

Answers

Answer 1
First, we are going to use the Pythagorean identity: [tex]sin^2(x)+cos^2(x)=1[/tex] to rewrite our expression. Solving for [tex]sin^2(x)[/tex] in our Pythagorean identity  we get that [tex]sin^2(x)=1-cos^2(x)[/tex], so we can rewrite our expression as follows:
[tex] \frac{1}{ \sqrt{1-cos^2(x)} } = \frac{1}{ \sqrt{sin^2(x)} } = \frac{1}{sin(x)} [/tex]

Next, we are going to use the trig identity: [tex]csc(x)= \frac{1}{sin(x)} [/tex] to completely simplify our expression:
[tex] \frac{1}{sin(x)} =csc(x)[/tex]

We can conclude that [tex] \frac{1}{ \sqrt{1-cos^2(x)} }=csc(x)[/tex]

Related Questions

When finding out if 2 triangles are congruent, is it possible to only use a side and angle if those are the only 2 provided? Help ASAP please.

Answers

Short answer: No and yes. 
Yes First.
If the lower right point (looks like an C perhaps or an F) and the middle point and the upper left point lie on the same line and if D the middle point and the upper right point lie n the the same line, then yes. You have angle side angle. The lower right angle is given as equal to the upper left angle. The angles at C are vertically opposite angles and they are equal and you have been given 2 enclosed sides that are equal.

No
If the points I've described are not on the same line, then the triangles are not congruent. If I can, I'll edit this a second time. 

Please Note:
You have done something that looks a bit illegal to me. I wouldn't just trade pictures. It only costs you another 5 points to issue another question. I do think, however, that it is very clever. In answering about 1700 questions, I've never seen this done. That's commendable.

What’s the largest fraction in each group?
a. 5⁄6 and 29⁄36
b. 5⁄12 and 3⁄8
c. 2⁄5 and 19⁄45
d. 5⁄7, 13⁄14, and 19⁄21
e. 7⁄11 and 9⁄121
f. 1⁄2, 3⁄18, and 4⁄9

Answers

To find the biggest fraction you need to convert them to decimals.
a) 5/6
b) 5/12
c) 19/45
d) 13/14
e) 7/11
f) 1/2
Hope this helps!

A rectangle has vertices at these coordinates

. (−6, 10), (−6, 1),(1, 10)

What are the coordinates of the fourth vertex of the rectangle?

Enter the coordinates in the boxes.

( , ​ ​)

Answers

The fourth coordinate point would be at (1, 1).  If you look at the graph, it's easy to see which point is missing.  You can also tell by looking for the x and y values that don't repeat, since this is a rectangle.  -6 is an x-value for two coordinate points, but 1 is an x-value for only one.  10 repeats as a y-value in two coordinate points, but 1 only appears once.

Answer:in knew it but i forgot

Step-by-step explanation:

there are 3 black marbles in and 4 red marbles in a bag. what is the probability that you will pick two black marbles put of the bag without replacing the first one?

Answers

[tex] |\Omega|=7\cdot6=42\\
|A|=3\cdot2=6\\\\
P(A)=\dfrac{6}{42}=\dfrac{1}{7}\approx14\% [/tex]

(7,1,9,52,12,25,9,7,7)what are the outliers?

Answers

52, 25 are the outliers


Which of the following equations represent a proportional relationship
a: y=12.5x
b: y= 4x-1
c: x+y=3
d: y=3x (squared)

Answers

A would be fine as your answer.

Use the law of cosines to explain why c^2=a^2+b^2 for triangle ABC, where angle C is a right angle.

Answers

Let [tex]c[/tex] be the length of the hypotenuse in the right triangle [tex]ABC[/tex], with [tex]m\angle C=90^\circ[/tex] for [tex]\angle C[/tex], the angle opposite the hypotenuse.

By the law of cosines,

[tex]c^2=a^2+b^2-2ab\cos C[/tex]

But [tex]\cos90^\circ=0[/tex], so we end up with [tex]c^2=a^2+b^2[/tex].

Can someone please help me with this?

Answers

I believe it is -8 since the point where the line is x=80 and y=-10. Then you divide x/y (80/-10) and get -8.
y=-10/80x because since the formula is y=mx+b m being slope and b being the y intercpet and since the y intercpet is 0 becuase the equation touches the y axis at 0, you dont need to include it and the slope is rise over run y/x so from the point -80,10 to 0,0 the fall is 10 becuase the line is going down so its -10 and its going to the right 80 times so its 80 so with -10 being the y and 80 being the x you divide -10 by 80 so just write it as -10/80 as it is accepted

A bag contains a total of 25 marbles. Five of the marbles are blue, 3 are red, 8 are green, and 9 are white. If a marble is drawn from the bag and then replaced 50 times, about how many times would a green marble be drawn?
A. 4
B. 8
C. 16
D. 24

Answers

There is an 8/25 chance of drawing a green marble, and since the marbles aee being drawn 50 times, then you have to muliply 8 by 2 to get 16/50. Since the marble is replaced after it’s drawn, the chances of drawing a green marble stay the same with each new pick, so 16/50 probability means that about 16 marbles will be drawn. (C)

Which substance traps pathogens and prevents them from entering the deeper tissue of the body? tears

Answers

i think it's mucus bc it's secreted from the goblet cells in the lining of the trachea(?) and traps bacteria and unwanted materials. im not sure tho.

Answer:

Mucus

Step-by-step explanation:

A 25 foot ladder leans against a wall 7 feet from the base of the wall. How high does the ladder touch?

Answers

a² + b² = c²

a² + 7² = 25²

a² = 25² - 7²

a² = 576

a = 24

Answer: The height is 24 feet.

The height formed by this 25 foot ladder that leans against a wall is 24 feet.

Given the following data:

Length of ladder (hypotenuse) = 25 foot.Adjacent = 7 feet.

What is Pythagorean Theorem?

Pythagorean theorem can be defined as a fundamental mathematical expression in Euclidean geometry that can be used to determine any of the three (3) sides of a right-angled triangle.

Mathematically, Pythagorean's Theorem is given by this formula:

[tex]h^2 = a^2 + b^2[/tex]

Where:

h is the hypotenuse.a is the adjacent side.b is the opposite side.

Substituting the given parameters into the formula, we have;

[tex]h^2 = a^2 + b^2\\\\25^2 = 7^2 +b^2\\\\625=49+b^2\\\\b^2=625-49\\\\b=\sqrt{576}[/tex]

b = 24 feet.

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If the sum of three numbers is 144, what is the average of the three numbers?   

Answers

The average will always be 48. No matter what the numbers are, they will equal 144 and there will always be 3 numbers so you divide 144 by 3 and that equals 48.

Final answer:

The average of three numbers that sum to 144 is 48, found by dividing 144 by 3.

Explanation:

The average of three numbers is the sum of those numbers divided by three. In this case, if the sum of three numbers is 144, then the average can be found by dividing 144 by 3. Calculating this, we get the average, which is 48 (144 ÷ 3 = 48). Hence, the average of the three numbers is 48.

First to answer with work shown gets Brainliest

Answers

I worked it out as shown:

In a recent fundraising campaign, Rise Over Run received 20 checks of various amounts to donate to their favorite charities. Olive uses this spinner to determine which charity will receive each check.
About how many of the 20 checks should arise Over Run expect to go to their TreeHuggers Campaign ?

Answers

Answer:

6 checks

Step-by-step explanation:


The expected number of checks out of 20 checks that should arise Over Run expect to go to their TreeHuggers Campaign is given by: Option D: 6 checks.

How to find that a given condition can be modeled by binomial distribution?

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

The expected value and variance of X are:

[tex]E(X) = np\\ Var(X) = np(1-p)[/tex]

For this case, we're specified that:

The spinner has 10 parts.

3 belong to Treehuggers2 belong to Ameriteach5 belong to Paws of Peace

Thus, the probability of getting the spinner fall on treehugger is 3/10 (three favorable parts of spinner to ten total parts, all parts assumingly equally probable and spinner assumingly not falling in the mid of two parts).

20 checks, all will be accompanied with 20 spins, all independent of each other.

Let X = total number of times the spinner falls on Treehuggers

And let Success for a spin = It landing on Treehugger

Failure for a spin = It not landing on Treehugger

Probability of success = p = 3/10 = 0.3Probability of faillure = 1-p = 7/10 = 0.7

n = 20, so we get:

[tex]X \sim B(n=20,p=0.3)[/tex]

The expected number of checks out of 20 checks that should arise Over Run expect to go to their TreeHuggers Campaign = expected number of successes in those 20 spins =  the expected number of values of X.

Since X follows a binomial distribution, we get:

[tex]E(X) = np = 20 \times 0.3 = 6[/tex]

Thus, the expected number of checks out of 20 checks that should arise Over Run expect to go to their TreeHuggers Campaign is given by: Option D: 6 checks.

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how do I find circumference

Answers

Given the radius (r) or diameter (d), you can find the circumference using:

C=2pi•r
or
C=pi•d

write an expression that represent the sum of r and 7

Answers

"The sum of r and 7" can be represented as r + 7

Final answer:

The expression that represents the sum of r and 7 is written simply as r + 7. This is a basic operation in algebra involving the addition of a variable and a constant.

Explanation:

To write an expression that represents the sum of r and 7, you simply add these two together. The mathematical expression for this is r + 7. This is a basic algebraic expression that demonstrates how to represent the addition of a variable, in this case r, with a constant number, which is 7.

just say answer, no need to explain! Thanks!

Answers

The given function is 

f(x) = |x|

Moving 4 units to right means, subtracting the number from x. So moving |x| 4 units to right will give:

f(x) = |x-4|

Moving 2 units up means addition of a number to the function. So moving 2 units up will give:

f(x) = |x-4| + 2

Thus, the correct answer to the question is option B

Given the two expressions shown below:

square root of 64 plus square root of 5
square root of 64 plus square root of 4

Which statement best describes the two expressions?
Both are rational.
Both are irrational.
A is rational, but B is irrational.
A is irrational, but B is rational.

Answers

Hi there!
The answer is A is irrational, but B is rational.

An irrational number is a number that cannot be written as a fraction.

Expression A.
[tex] \sqrt{64} + \sqrt{5} = 64 + 2.23606...[/tex]
This cannot be written as a fraction and therefore the expression is irrational.

Expression B.
[tex] \sqrt{64} + \sqrt{4} = 8 + 2 = 10 = \frac{10}{1} [/tex]
This can be written as a fraction and therefore the expression is rational

Your answer:
A is irrational, but B is rational.

~ Hope this helps you!
MarkV

Answer:

A is rational, but B is irrational.

Step-by-step explanation:

just answer no need to explain.

Answers

Shifting to left mean adding the number from each occurrence of x from the given function.

So, shifting x³ , 3 units to left will result in:

f(x) = (x + 3)³

Shifting down means subtracting the number from the function value. 

So, shifting 2 units down will result in:

f(x) = (x + 3)³ - 2

Therefore, option A is the correct graph



I think it would be answer b. [tex]f(x)=(x+3)^2-2[/tex]

How many prime numbers between 8 and 60 leave a remainder of 2 when divided by 6?

A) 0
B) 1
C) 4
D) 6
E) 7

Answers

Hey there!! :D




Prime Number: Is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.




If you list out all of the prime numbers between 8 and 60 and divide each one by 6, you will notice that the remainder ends with either 1or 5 and not 2.



So your answer would be A) 0



Hope this helps!!

Have A Fantastic Weekend!!

how many lines of symmetry does the flag of Iraq have

Answers

1, (and it’s down the center Vertically)

Final answer:

The flag of Iraq has no lines of symmetry due to its horizontal stripes of different colors and the specific orientation of the Arabic Kufic script of the Takbir written in the center.

Explanation:

The question about how many lines of symmetry the flag of Iraq has can be classified as a question in the field of mathematics, particularly in the study of geometry. Symmetry in flags can pertain to reflections across certain lines where the flag is indistinguishable from its mirror image.

As of my knowledge update, the flag of Iraq consists of three horizontal stripes of red, white, and black, with the Takbir ('Allahu Akbar') written in the center in green Kufic script. As the script introduces a specific orientation and the colors do not symmetrically repeat, the flag does not have horizontal or vertical lines of symmetry. The presence of textual elements disrupts potential symmetry, considering the particular way letters must be oriented to be readable. Hence, the flag of Iraq does not have any lines of symmetry.

Max donated 16 dog collars to the dog shelter. Mia donated some leashes. How many items does Mia need to donate that would require you to regroup to find the total number of items donated?

Answers

16 I am pretty sure is the answer

Mia can donate up to 4 leashes without requiring regrouping to find the total number of items donated.

To determine how many leashes Mia needs to donate such that you would need to regroup to find the total number of items donated, we need to know the maximum capacity of the shelter's storage or the maximum number of items that can be comfortably accommodated without regrouping.

If we assume that the shelter's storage can hold a maximum of 20 items comfortably without needing to regroup, then we can calculate the number of items Max and Mia can donate without regrouping:

Max donated 16 dog collars, and the shelter can accommodate 20 items without regrouping. So, Max has donated within the capacity without needing to regroup.

Now, let's see how many leashes Mia can donate without exceeding the capacity:

20 (maximum capacity) - 16 (Max's donation) = 4

Mia can donate up to 4 leashes without requiring regrouping to find the total number of items donated. If Mia donates more than 4 leashes, you would need to regroup to calculate the total number of items donated.

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Write an inequality to represent this situation: The temperature stayed above -15 degrees.

Answers

Hoi!

I will use t to represent the temperature.

Your inequality is t > -15

But why?

This is because the temperature, if staying above -15, would be greater than -15, hence the "greater than" symbol. Since t is the value mentioned first in our little word problem, we would put that first. :)

plzzzz help!!!!!!!!!!!!!

Answers

Answer:

x + 2 is in both the numerator and the denominator, so the correct answer is A.

Written as a percent , what is the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5

Answers

1, 3, and 5 are the odd numbers so the fraction would be 3/5. If you multiply the numerator and denominator by 20 you get 60/100, which would give you 60%

The probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5 is, 60%

What is mean by Probability?

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

To find the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5.

Since, From 1 to 5, there are three numbers 1, 3, 5 are odd numbers.

Hence, the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5 is,

P = 3/5

Change into percent as;

P = 3/5 x 100%

P = 60%

Thus, the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5 is, 60%

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A professional basketball team must play a total of 85 came before the playoffs begin. The team has played 3/5 of the scheduled games, if the team plays 10 more games, what is the total number of games they will have played

Answers

Final answer:

After calculating the number of games already played as a fraction of the total and adding 10 more games, it is determined that the team will have played 61 games.

Explanation:

The subject of this question is Mathematics, particularly it involves operations with fractions. The team has played 3/5 of the total scheduled games. So let's calculate how many games that would be by multiplying the total number of games, 85, by 3/5:

The team has already played 85 * 3/5 = 51 games.

If the team plays 10 more games, we need to add this to the number of games already played:

51 (already played games) + 10 (more games) = 61 games.

Therefore, the total number of games the team will have played after 10 more games is 61 games.

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at the pet shelter,for every 7 dogs there are 5 cats.what is the ratio of dogs to cats?
a.5:7
b.7:5
c.7:12
d.12:7

Answers

B Because there a 7 dogs and five cats
The answer would be B. When it asks Dogs to Cats. The value for dogs would go first. If it was cats to dogs the cat value would be first

what is the relationship of 7 and -7

Answers

There are opposites
They are a zero pair! They are opposites! The absolute value of -7 is 7! 
Hope this helps!

Samantha is installing a new window in her bedroom wall. She wants to center it horizontally. the window is 40.5 inches long, and the wall is 105.25 inches long. how far from each edge of the wall should Samantha install the window?

Answers

The wall length- window length = 105.25- 40.5 = 64.75

To center the window horizontally on a wall, subtract the window's length from the wall's length and divide by two. Samantha should install the window 32.375 inches from each edge of the wall.

The student is trying to determine how far from each edge of the wall she should install the window to center it horizontally. To find this, we calculate the difference between the wall's length and the window's length and then divide that number by two. The wall is 105.25 inches long, and the window is 40.5 inches long.

To center the window horizontally, we do the following calculation:
(Length of wall - Length of window) / 2
(105.25 inches - 40.5 inches) / 2
64.75 inches / 2
= 32.375 inches.

Therefore, Samantha should install the window 32.375 inches from each edge of the wall to center it horizontally. This calculation ensures the window is positioned equally from both sides of the wall, assuming the wall is straight and the measurements are accurate.

solve the equation for a
w=7a+4b

Answers

w=7a+4b
w-4b = 7a
[tex]a= \frac{w-4b}{7}[/tex]

The linear equation for "a" in terms of "w" and "b" is:

a = (w - 4b) / 7By following these steps, we have solved the linear equations for "a" and expressed it in terms of "w" and "b."

To solve the equation for "a" in terms of "w" and "b," we can follow these steps:

Step 1: Start with the equation:

w = 7a + 4b

Step 2: Isolate the term with "a" on one side of the equation. To do this, subtract 4b from both sides:

w - 4b = 7a

Step 3: Divide both sides of the equation by 7 to solve for "a":

(w - 4b) / 7 = a

Step 4: Simplify the expression:

a = (w - 4b) / 7

Therefore, the linear equation for "a" in terms of "w" and "b" is:

a = (w - 4b) / 7By following these steps, we have solved the linear equations for "a" and expressed it in terms of "w" and "b."

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