Find sin(2x), cos(2x), and tan(2x) from the given information.
sin(x) = [tex]-\frac{3}{5}[/tex] for [tex]\frac{3\pi }{2}[/tex] < x < 2

Answers

Answer 1

I assume 3π/2 < x < 2π, so that x is in the 4th quadrant. For angles x terminating in Q4, we have sin(x) < 0 and cos(x) > 0, so tan(x) = sin(x)/cos(x) < 0.

This means that, using the Pythagorean identity,

cos(x) = + √(1 - sin²(x)) = 4/5

tan(x) = (-3/5) / (4/5) = -3/4

Recall the double angle identities:

sin(2x) = 2 sin(x) cos(x) = 2 (-3/5) (4/5) = -24/25

cos(2x) = 2 cos²(x) - 1 = 2 (4/5)² - 1 = 7/25

tan(2x) = 2 tan(x) / (1 - tan²(x)) = 2 (-3/4) / (1 - (-3/4)²) = -24/7


Related Questions

ALGEBRA 2:

"As you may know, Ms. Gran is our hottest movie star of the century. This agency considers it our good fortune to have her as one of our clients. Since she is in such big demand the movie studio of ILM will do anything to get her under contract. Because of this, they have sent over three different contracts for her. Since math was your favorite subject in school, I am asking that you analyze the three contracts to help Ms. Gran make the best financial decision. When you have completed your analysis, I need you to send a report to Ms. Gran explaining what you think is in her best interest to sign."

Contract A:

$20 for a 1 day contract
$40 for a 2 day contract
$80 for a 3 day contract, etc.

Contract B:

$0.02 for a one day contract
$0.06 for a two day contract
$0.18 for a three day contract, etc.

Contract C:

$100,000 for a 1 day contract
$200,000 for a 2 day contract
$300,000 for a 3 day contract, etc

Answers

Step-by-step explanation:

it is 300,000 for a 3 day contract

10.A water tank has strps inside it. A monkeyis sitting on topmost floor(i.e.,the first step).The water level is at ninth step. (ii)After drinking water,he wants to go back 2 steps down in every move.In how many jumps will he reach back the tops step?​

Answers

Answer:

11 id.k i think

Step-by-step explanation:

i think that it

Solve the system of equations.


2x−9y=14
x=−6y+7

Answers

Step-by-step explanation:

[tex]put \: x \: into \: equation \: 1[/tex]

[tex]2( - 6y + 7) - 9y = 14[/tex]

[tex] - 12y + 14 - 9y = 14[/tex]

[tex] - 21y + 14 = 14[/tex]

[tex] - 21y = 14 - 14[/tex]

[tex] - 21y = 0[/tex]

[tex] \frac{ - 21y}{12} = \frac{0}{21} [/tex]

[tex]y = 0[/tex]

[tex]put \: y = 0 \: into \: equation \: 2[/tex]

[tex]x = 6y + 7[/tex]

[tex]x = 6(0) + 7[/tex]

[tex]x = 0 + 7[/tex]

[tex]x = 7[/tex]

Answer:

y = 0

x = 7

Step-by-step explanation:

2x − 9y = 14     ⇒  ( 1 )

x = − 6y +7      ⇒ ( 2 )

First, let us find the value of y.

For that, replace x with ( - 6y + 7 ).

Let us take equation 1 for that.

2x − 9y = 14

2 ( - 6y + 7 ) - 9y = 14

-12y + 14 - 9y = 14

21y = 14 - 14

21y = 0

Divide both sides by 21.

y = 0

And now let us take equation 2 to find the value of x by replacing y with 0.

2x − 9y = 14    

2x - 9 × 0 = 14

2x - 0 = 14

2x = 14

Divide both sides by 2.

x = 7

Tammy took a total of 14 quizzes over the course of 7 weeks. ​ ​How many weeks of school will Tammy have to attend this quarter before she will have taken a total of 18 quizzes? ​ ​Solve using unit rates. ​Answer: weeks.

Answers

Answer:

9 weeks

Step-by-step explanation:

So he basically took 14 quizzes in 7 weeks.

14/7 = 2/quizzes per week

18/2 = 9 weeks

I don't know what you mean by unit rates but this is what I got.

Transform the table below given that g(x) = 2 f(6x).+ 8. Enter your answers as reduced fractions if necessary. Make sure your answers line up vertically with the corresponding x and f(x) values. As a hint, you can consider y f(x) to be the base graph of g(x).​

Answers

The function g(x) = 2f(6x) + 8 is a function transformation of the function f(x)

How to transform the table?

The function g(x) is given as:

g(x) = 2f(6x) + 8

The table is not given.

So, I will provide a general explanation

Using the following values of x:

x = 0, 1, 2, 3......

We have:

g(0) = 2f(6 *0) + 8

g(0) = 2f(0) + 8

g(1) = 2f(6 *1) + 8

g(1) = 2f(6) + 8

g(2) = 2f(6 *2) + 8

g(2) = 2f(12) + 8

g(3) = 2f(6 *3) + 8

g(3) = 2f(18) + 8

Next, we assume the following values

f(0) = 4, f(6) = 5; f(12) = 6 and f(18) = 7

The values become:

g(0) = 2f(0) + 8 = 2 * 4 + 8 = 16

g(1) = 2f(6) + 8 = 2 * 5 + 8 = 18

g(2) = 2f(12) + 8 = 2 * 6 + 8 = 20

g(3) = 2f(18) + 8 = 2 * 7 + 8 = 22

So, the table of values would be:

x     g(x)

0     16

1     18

2   20

3   22

Read more about function transformation at:

https://brainly.com/question/4025726

Good people please help me!!!! ​

Answers

Answer:

P=90°

R=45°

Step-by-step explanation:

PQR=180°

180°-45°=135°

R=45°(iscoles triangle)

P=90°

(d) (1 + cos a) (1 - cos a) /(1 + sin a) (1 - sin a)= tan2 a​

Answers

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

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

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

[tex] {tan}^{2} (a)[/tex]

i need this with the steps

Answers

3x>16+8
3x>24
3/3x>24/3
x>8

Please Helpp!!!! Pythagorean theorem

Answers

Answer:

12.6 = c

Step-by-step explanation:

The Pythagorean therom is a^2 + b^2 = c^2

We already know 2 varibles (12 and 4) so we can just plug them in.

12^2 + 4^2 = c^2

144 + 16 = c^2

160 = c^2

[tex]\sqrt{160}[/tex] = [tex]\sqrt{c^2}[/tex]

12.6 = c

Hope this helps :)

Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Which equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x?

y=4+x
y = x − 4
y = 4 · x
y = x ÷ 4

Answers

Answer:y=4+x

Step-by-step explanation:

You are adding gallons not *,/,-,. So it's y=4+x.

The required equation is y = 4 + x. The correct answer would be an option (A).

What is an equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Jayne stopped for gas before embarking on a road trip. There were already 4 gallons of gas in the tank.

As per the question, the required equation would be as:

y = 4 + x

This equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x. The total amount of gasoline in the tank, y, is equal to the number of gallons that she put in the tank, x, plus the 4 gallons that were already in the tank.

Learn more about the equation here:

brainly.com/question/10413253

#SPJ2

What is the smallest number which is reversed when 2 is added to its double?

Answers

Answer:

25

Step-by-step explanation:

Let the number be 10x+y.

So we have 2(10x+y)+2 = 10y+x, or

20x + 2y + 2 = 10y+x, or

19x=8y-2 …(1)

Try different values of x which satisfy (1) giving an integer value of y. Moreover x should be less than y. The only value of x is 2 which gives us y = 5.

So y = 5 and x = 2.

And the answer is 25.

We can prove this by simply doing the question's equation:

50(since it's the double of 25) + 2 =

50+2= 52

Hope this helps

A biologist is studying the exponential growth of a colony of bacterial cells. The table gives the
number of cells, y, in the colony over time, x, in hours.
Time, x (hours)
0
Number of Cells, y
100
1
200
N
400
h
6,400
Replace the values of A, b, x, and y to write an exponential equation that represents the number of
cells present at h hours.

Answers

The exponential function that represents the number of cells present at x hours is y = 100(2)ˣ

What is an exponential function?

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

Let y represent the number of cells after x hours.

From the table, at point (0, 100):

100 = ab⁰

a = 100

At point (1, 200):

200 = 100b

b = 2

The exponential function is y = 100(2)ˣ

Find out more on exponential function at: https://brainly.com/question/12940982

Answer:

100(2)^h=6,400

Step-by-step explanation:

Explanation:

For an equation in the form A(b)^x=y, A represents the initial amount, and b represents the growth rate. At 0 hours, there were 100 cells, so A=100.

Between 0 hours and 1 hour, the number of cells doubled from 100 to 200, or 100(2). Between 1 and 2 hours, the number of cells again doubled from 200 to 400, or 100(2)^2. So the growth rate, or b, is 2.

The table shows that at h hours, there were 6,400 cells. Therefore, the equation that represents the number of cells at h hours is .100(2)^h=6,400

Based on the pattern, which power of 10 would have a value of StartFraction 1 Over 1,000,000 EndFraction?

Answers

Answer:

powers of 10

Step-by-step explanation:

Simone examined the pattern in the table

Brendan is building a dog house, and the
dimensions of the roof are shown below. What is
the lateral surface area of the roof?
2.7f
5 ft
3 f+
A. 24.84 f+2
B. 46 f+2
C. 54.1 f+2
D. 43.2 f+2

Answers

Answer:

B. 46 ft²

Step-by-step explanation:

Two sides are rectangles 3.1 ft by 5 ft.

One side is a rectangle 5 ft by 3 ft.

area = 2(3.1 ft × 5 ft) + (5 ft × 3 ft)

area = 46 ft²

Madelyn has 4 pairs of red socks, 6 times as many pairs of blue socks 1 as white pairs of socks, and I as many white pairs as red pairs. How many pairs of socks does she have in all? How many socks does Madelyn have?​

Answers

The Total Number of socks is 10 in all, bear in mind that there is no blue socks hence it will not add to the total amount of socks

Addition of Numbers

Note : 1 pais = 2 socks

Given Data

Red Socks = 4 pairs = 4*2 = 8 socks 6 times as many pairs of blue socks = 0 1 as many pairs of  white socks = 2 socks

The statement " 6 times as many pairs of blue socks" is equivalent to no socks, since we have no blue socks, hence 6*0 = 0

Let us find the total socks

= 8+0+2

= 10 socks

Learn more about addition here:

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Please help i am begging

Answers

x is equal to 3 ..

Step-by-step explanation:

hope this helps

Find the simple Intrest for
​$ 2000 at 4​% for 3 months

Answers

Answer:

Simple interest: 240, Final amount: 2240

hope im right

Step-by-step explanation:

help pls quick i need the answer pls

Answers

Answer:

multicultural

Step-by-step explanation:

Answer:

A. Multicultural

Step-by-step explanation:

It shows later in the sentence that they ate Thai noodles and Egyptian falafel those come from different cultures so it must be multicultural

I really need help now. 100 points plus brainly if correct. I GOT THINGS TO DO!!! Answer the question in the picture

Answers

Answer: 4,000

Step-by-step explanation:

The only logical choice there because of the rate of others

Answer: c is the answer

Step-by-step explanation:

can someone help me solve this logarithm function

Answers

Answer:

[tex]\boxed{\sf{x=\dfrac{25}{2}=12.5}}[/tex]

Step-by-step explanation:

Solve the logarithm function.

Put the logarithm function on one side of the equation and x on the other.

log x + log8=2

[tex]\sf{\log _{10}(x)+\log _{10}(8)=2}[/tex]

First, subtract by log₁₀(8) from both sides.

[tex]\sf{\log _{10}(x)+\log _{10}(8)-\log _{10}(8)=2-\log _{10}(8)}[/tex]

Solve.

[tex]\sf{\log _{10}(x)=2-\log _{10}(8)}[/tex]

[tex]\sf{\log _{10}(x)=2-\log _{10}(8)=\boxed{\sf{x=\dfrac{25}{2} }}[/tex]

Therefore, the correct answer is x=25/2=12.5.

I hope this helps you! Let me know if my answer is wrong or not.

These diagrams show the dimensions of two different windows. Which of the following statements are true? Choose all that apply.
Window A
3 ft
8 ft
Window
B
4 ft
6 ft
O A. The windows have the same area.
B. The perimeter of Window A is less than the perimeter of Window B.
C. The perimeter of Window B is 20 feet.
OD. The area of Window A is 22 square feet.

Answers

A, and C is the answer

write the ratio as a fraction in simplest form

Answers

14/27. I have linked my working our down below make sure to have a look at it for a better understanding.

What is the solution to x^3 + 4x^2 > x + 4?

Answers

Answer:

-4 < x < -1 or x > 1 (the third option)

Step-by-step explanation:

hope this helps

Find two positive numbers whose product is 192 and their sum is a minimum.

Answers

Answer:

8√3

Step-by-step explanation:

Let a, b = the positive numbers, and the sum = s,

(1)---- ab = 192

(2)--- a + b = s

Since we want to find the minimum sum, we'll have to substitute one of the variables (either a or b) from (1) to (2), I'll choose b,

From (1), b = 192/a

Substitute b = 192/a into (2),

s = a + 192/a

Now, we are able to use a concept of calculus (maximum & minimum) to solve it, just remember 2 steps in finding the values of x in maxima minima question:

1) find dy/dx

2) Find x from dy/dx = 0

ds/da = 1 - 192/

When ds/da = 0,

1 - 192/ = 0

= 192

a = ±192

a = 83 , -83

Since a is positive, a = 83

Substitute a into (1),

b = 192/(83)

b = 83

Therefore, the two positive numbers are 8√3... and 8√3

A pianist plans to play 5 pieces at a recital from her repertoire of 27 pieces. How many different recital programs are possible?

Answers

The different recital programs that are possible is 80,730 ways

Combination and permutation

Permutation has to do with arrangement while combination has to do with the selection.

According to the question, a pianist plans to play 5 pieces at a recital from her repertoire of 27 pieces, this shows that he can select the 5 pieces in any form.

The number of ways this can be done is given as:
[tex]27C_5=\frac{27!}{(27-5)!5!}\\ 27C_5=80,730[/tex]

Hence the different recital programs that are possible is 80,730 ways

Learn more on combination here: https://brainly.com/question/11732255

PLEASE HELP PLEASE HELP

Answers

Answer:

The answer should be 15, since each week the number goes up by 15.

I see a pattern here! Let me show you - multiply 15 by the week number (1, 2, 3, 4, ...), and you have y.

For example, 15 x 3 (for week 3) is 45, as shown by the y value.

So all we must do is multiply 15 by 5, and voila! We'll have our answer. Which, by the way, is 75.

I hope this answers your question!

-Toremi

• Identifică, în fiecare plan al clasei, obiectul care nu este reprezentat. Scrie în caiet numele acestuia. ​

Answers

Answer:

a

Step-by-step explanation:

An asteroid is a minor planet of the inner Solar System. Historically, these terms have been applied to any astronomical object orbiting the Sun that did not resolve into a disc in a telescope and was not observed to have characteristics of an active comet such as a tail.

If you deposit `\$300` in an account and it grows by `6\%` each year, how much money will be in your account after `1` year?

Answers

Answer:

$318

Step-by-step explanation:

6% x 300 = 18

300 + 18 = 318

On a coordinate plane, DEF has vertices D(1,2), E(7,2)and F(1,9). What is the distance between point E and F?

Answers

Step-by-step explanation:

Using distance formula,

Let the distance between point E and F = ef,

[tex]ef = \sqrt{{(7 - 1)}^{2} + {(2 - 9)}^{2} } \\ ef = \sqrt{85} \\ = 9.219544457[/tex]

Find the area and perimeter of the figure below.

Answers

Answer:

x to the 3rd power

Step-by-step explanation:

x+x to the 2nd power = x to the 3rd power

Step-by-step explanation:

The area is the sum of three figures

A = 1*1 + 1*x + x²

   = x² + x + 1

The perimeter is the sum of border segments

P = x*4 + 1*4

  = 4x + 4

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