–sin2(x) = cos(2x) from [–π,π]

I need help on this

Answers

Answer 1

If the equation is

- sin²(x) = cos(2x)

rewrite the left side using the Pythagorean identity,

sin²(x) = 1 - cos²(x)

and the right side using the double angle identity for cosine,

cos(2x) = 2 cos²(x) - 1

Then the equation transforms to

- (1 - cos²(x)) = 2 cos²(x) - 1

Solve for cos²(x) :

-1 + cos²(x) = 2 cos²(x) - 1

cos²(x) = 0

Take the square root of both sides to get

cos(x) = 0

Solve for x :

x = cos⁻¹(0) + 2   or   x = cos⁻¹(0) - π + 2

x = π/2 + 2   or   x = -π/2 + 2

where n is any integer. We get solutions in the interval [-π, π] when n = 0, giving the solutions

x = π/2   or   x = -π/2


Related Questions

8. Lisa types 6 pages in 36 minutes. Frank types 5 pages in 30 minutes. Do they type at the same rate? Use a proportion to explain.

Answers

Answer:

Yes

Step-by-step explanation:

Lisa and Frank type at the same rate.

They both type 1 page every six minutes.

Lisa types 6 pages every 36 minutes, and if we divide the minutes by the pages, we get

[tex]\frac{36}{6} = 6[/tex]

And Frank types 5 pages ever 30 minutes, when we divide we get

[tex]\frac{30}{5} = 6[/tex]

Select Yes or No to indicate whether each of the ordered pairs is most likely a solution to the equation represented by the graph.

Answers

Yes, yes, no I believe

For a Biology assignment, Lisa collected data on plant growth of a sunflower every week for 9 weeks. When Lisa first planted the sunflower, it was 10 centimeters tall. The time (in weeks) is plotted against the height (in centimeters) as shown below. Using the best-fit line, approximately how tall was the sunflower plant during the fifth week? 33 centimeters 34 centimeters 35 centimeters 30 centimeters

Answers

Answer:

I think it was 34 cm because it should be not too long

Step-by-step explanation:

this is from my logic perspective

0.5= x djdododododododdodod

Answers

Answer:

25

Step-by-step explanation:

cuz

1) -1 = x – 5
2) -5x + 2 = 17

PLS ANSWER PLS PLS PLS

Answers

Are you trying to do substitution or elimination?

Plzzz answer it :( :

All fraction or mixed number answers are in simplest form or reduced form .

True or false

Answers

Answer:

false it is not always reduced form

false it doesn’t always have to be reduced

Maggie is participating in her school reading challenge. She reads 80 books in 6 months. If 40 of the books are fiction, then what percent of the books that she read are fiction?

Answers

Answer:

50%

Step-by-step explanation:

*In this question, the 6 does not matter*

If 40/80 books are fiction, and if you simplify that fraction, you get 1/2.

Percentages are just fancy fractions and decimals. 50% means 1/2.

Thus, the answer is 50%

Delete this already.

Juanita earns $36 for 3 hours of work. At that rate, how long would she have to work to earn $720?

Answers

Well it would be 7 days. 36 x 3 is 108 720 divided by that is 6 but a remainder so you add one to 6 and it’s 7

Answer:

She has to work for 60hours in order to earn $720.

Step-by-step explanation:

Amount of money earned in 1hour=36÷3

                                                        =12$

Total time required=720÷12

                               =60hours

pitcher can hold 1,200 milliliters of tea. How many liters of tea are in the pitcher?​

Answers

Answer:

1.2 Liters

Step-by-step explanation:

There are 1000 mL in 1 L. divide 1200 by 1000 and you get 1.2

Given
f
(
x
)
=

x

3
f(x)=−x−3, solve for
x
x when
f
(
x
)
=

2
f(x)=−2.

Answers

Answer:

-5

Step-by-step explanation:

Substitute every part of the equation where x appears with the value of x, which is -2

f(-2)=-2-3

f(-2)=-5

So, f(x)=-5

The answer is -5 I hope this helps

MY HRW ‼️ Solve the equation. You may find using algebra tiles helpful in solving this problem.
X +6=-X-6

Answers

Answer:

x=-6

Step-by-step explanation:

x+6=-x-6

(-6)+6=(6)-6

0=0

Answer:

Solve the equation. You may find using algebra tiles helpful in solving this problem.  X +6=-X-6               X= -6

what is wswssssssssss 4+4?

Answers

Answer: 4+4=8

Hope this helps :)

Step-by-step explanation:

Say you have four apples, and your friend gives you four more. You put together the amount of apples you have and you get 8.

Help me with this plz!?!? I will mark brainliest!!!

Answers

If the temp is 12f and changes by -26f
Is 38f

HELP!!! STATS!!!
A random sample of 100 felony trials showed a sample mean waiting time between arrest and trial = 173 days with a population standard deviation of waiting times = 28 days. Find a 99% confidence interval for the population mean waiting time.

Stats question, I'm really stck please help me!

Answers

Answer:

The 99% confidence interval is   [tex] 165.776  <  \mu <  180.224  [/tex]  

Step-by-step explanation:

From the question we are told that

     The sample size is  n  = 100

     The sample mean is  [tex]\= x = 173 \ days[/tex]

      The population standard deviation is  [tex]\sigma = 28 \ days[/tex]  

From the question we are told the confidence level is  99% , hence the level of significance is    

      [tex]\alpha = (100 - 99 ) \%[/tex]

=>   [tex]\alpha = 0.01[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } = 2.58 [/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }[/tex]

      [tex]E = 2.58  *  \frac{28 }{\sqrt{100} }[/tex]

=>    [tex]E = 7.224 [/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\= x -E <  \mu <  \=x  +E[/tex]

=>     [tex] 173 -7.224  <  \mu < 173 + 7.224  [/tex]    

=>     [tex] 165.776  <  \mu < 180.224  [/tex]  

     

Look at the equation. y=2x−2 Which situation is best described by the equation?

A. The temperature at 2.00AM 2°c and rises 2°C each hour for x hours

B. The temperature at 2.00AM is -2°C and rises 2°C each hour for x hours

C.The temperature at 2:00AM is 2°C and drops 2°C each hour for X hours

D. The temperature at 2:00AM is -2°C and drops 2°C each hour for x hours.

Answers

Answer: A

Step-by-step explanation:y=2x−2 2.00AM 2°c and rises 2°C each hour for x hours

The largest prime number that is a factor of 35 is multiplied by the smallest prime number

Answers

Answer:

the largest factor of 35 is 35 and the smallest prime number is 2 so 35 times two is 70

Step-by-step explanation:

plz help! will give brainliest! really easy!

Answers

Answer:

C

Step-by-step explanation:

I explained it in the comments of the other one

Consider this function.
(r) = -3r + 3
Which graph represents the inverse of function ?

Answers

9514 1404 393

Answer:

  C.  graph Y

Step-by-step explanation:

Starting with f(r) = -3r +3, the inverse function can be found from ...

  r = f(y)

  r = -3y +3

  r -3 = -3y

  (r -3)/-3 = y

  y = -1/3r +1

The inverse function will have a slightly negative slope and a y-intercept of 1. This matches graph Y.

which of the following is a characteristic of the circumcenter of a triangle? multi-choice. A. it is the center of the only circle that can be inscribed in the triangle. , B. it is the center of the circle that can be inscribed in given a given triangle. C. it is the center of the only circle that can be circumscribed about the triangle. D. it is equidistant from all three sides of the triangle.

Answers

Answer:

C

Step-by-step explanation:

The circumcenter is called ”the circumcenter” because it is the center of the circle that ”circumscribes” the triangle.

I hope this helps!

Further explanation:

For a circle to circumscribe something, it circles it so that each of the vertices are on the circle, so each of the vertices are equidistant from the circumcenter. The circumcenter of a triangle is formed by the perpendicular bisectors of its sides.

Side note:

The rest of the choices describe an incenter.

Explain how to graph 8 is greater than it equal to y

Answers

Answer:

t w e n t y c h a r e c t e r s l o n g

need this done quick pls

Answers

Answer:

50 degrees

Step-by-step explanation:

40+50=130

130-180

50

Answer:

50

I have not done this in years!

Put these numbers in order from least to greatest.

3 4/5 3 3/4 3.5

Answers

Answer:

3/4, 4/5, 3, 3, 3.5

Answer:

3.5,3 3/4,3 4/5

Step-by-step explanation:

Least to greatest 0.4, 5/8, 74%, 3/5

Answers

Answer:

0.4,3/5,5/8,74%

Step-by-step explanation:

Change them all into decimals.

Get 0.4,0.625,0.74,0.6

Then reorder and see what their original values were

Christina has 50 coins consisting of quarters and dimes. The coins combined value is $9.50. Write a system of equation to determine how many quarters and dimes Christina has.

Answers

Answer:

Christina has 30 quarters and 20 dimes.

Step-by-step explanation:

Given that a quarter is worth 0.25 dollars and a dime is worth 0.10 dollars, if Christina has 50 coins and these add up to a total of $ 9.50, to determine the number of quarters and dimes that she has in her possession, the following calculation must be carried out, taking into account that the difference between a quarter and a dime is 0.15 dollars:

50 x 0.25 = 12.5

12.5 - 9.5 = 3

Thus, the difference between the value that Christina has and the value that she would have if all of her coins were quarters is 3 dollars. Thus, since 0.15 x 20 equals 3, of the 50 coins Christina has, 30 are quarters and 20 are dimes.

This is confirmed through the following equation:

30 x 0.25 + 20 x 0.1 = X

7.5 + 2 = X

9.5 = X

What is the value of x in the rhombus below?
O A. 17
O B. 35
O C. 53
O D. 37

Answers

Answer:

∴ x= 17

Step-by-step explanation:

the total of angel in 90°

∴ 2x+3+3x+2 =90

∴ 5x +5 =90

  5x=90-5

  5x = 85  (divide both side by 5)

∴ x= 17

Answer:17

Step-by-step explanation:

big brain knowledge

whats 7, −6, 4, −10, 3 least to greatest

Answers

Answer:

-10, -6, 3, 4, 7

Step-by-step explanation:

Hope it helps ^^

Need help geometric sequences see pic for details

Answers

Given:

The recursive formula of a geometric sequence is

[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex]

[tex]a_1=-3[/tex]

To find:

The explicit formula of the given geometric sequence.

Solution:

We know that, first term of geometric sequence is [tex]a_1=-3[/tex].

Recursive formula of a geometric sequence is

[tex]a_n=a_{n-1}\times r[/tex]      ...(i)

where, r is common ratio.

We have,

[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex]    ...(ii)

On comparing (i) and (ii), we get

[tex]r=\dfrac{1}{8}[/tex]

The explicit formula of a geometric sequence is

[tex]a_n=a_1r^{n-1}[/tex]

Putting [tex]a_1=-3[/tex] and [tex]r=\dfrac{1}{8}[/tex], we get

[tex]a_n=-3\left(\dfrac{1}{8}\right)^{n-1}[/tex]

Therefore, the correct option is D.

1/13 times 1/2.54 show your work

Answers

Answer:

0.03028467595

Step-by-step explanation:

calculator?

Stephanie needs to cover her yard with 410taft2of soil. She has enough for 125ft2in one bag and 65 ft2in another bag. How much more square feet of soil will she need covered?

Answers

Answer:

Stephanie needs 220ft² of more soil to cover the rest of her yard.

Step-by-step explanation:

First add the bags she already has:125ft²+65ft²+x=410ft² --> 190ft²+x=410ft²

Second use the subtraction property of equality: 190ft²-190ft²+x=410ft²-190ft² ---> x=220ft²

BRANLIEST TO CORRECT ANSWER!!!

Which statements describe vascular tissue?

Check all that apply.

The primary purpose of vascular tissue is to support the plant and help it stand upright.


Phloem carries food made during photosynthesis to other parts of the plant.


Phloem contains the chloroplasts.


Xylem moves water and nutrients throughout the plant.


Xylem is the protective, waxy layer on a plant that prevents water loss.

Answers

Answer:

Xylem moves water and nutrients throughout the plant.

Answer:

B and D

Step-by-step explanation:

most people in the comments said it was right so I tried it and got it right

Other Questions
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