2cos5xcos3x+sinx=cos8x

Answers

Answer 1

It looks like your equation (it's not an identity) is

2 cos(5x) cos(3x) + sin(x) = cos(8x)

Recall that

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

==>   2 cos(x) cos(y) = cos(x + y) + cos(x - y)

so that

2 cos(5x) cos(3x) = cos(8x) + cos(2x)

Then the equation simplifies to

cos(8x) + cos(2x) + sin(x) = cos(8x)

cos(2x) + sin(x) = 0

Also recall that

cos(2x) = 1 - 2 sin²(x)

so the equation is quadratic in sin(x) and can be factorized:

1 - 2 sin²(x) + sin(x) = 0

2 sin²(x) - sin(x) - 1 = 0

(2 sin(x) + 1) (sin(x) - 1) = 0

Solve for x :

2 sin(x) + 1 = 0   or   sin(x) - 1 = 0

sin(x) = -1/2   or   sin(x) = 1

[x = arcsin(-1/2) + 2   or   x = π - arcsin(-1/2) + 2]   or   x = arcsin(1) + 2

(where n is any integer)

x = -π/6 + 2   or   x = -5π/6 + 2   or   x = π/2 + 2


Related Questions

Can someone help me please like please I need to turn it in like in 10 minutes

Answers

Ima give you the graph points just put them there it’s (2,3) then (6,6) then (0,-2)

Use linear combination to solve for x and y.
2x+4y=-4
3x+5y=-3

Answers

Dautienbanchuyenvexophuongtrinhthu1saudothevaophuontrinhthu2,thuchiencacbuoc

chuyenvedoidaularaketquanhe

2x+4y=-4: x=-2-2y y=-1-x/2

3x+5y=-3: x=-1-5y/3 y=-3/5-3x/5

Samantha found a great deal on sweatshirts at the mall and bought 5 sweatshirts at the
Super Duper sale price. Allison went the next day, but the sale was over, so she only bought
2 sweatshirts and paid $30 more per sweatshirt than Samantha. If the total cost of all 7
sweatshirts was $340, how much did one sweatshirt cost at the Super Duper sale price?

Answers

Answer:

$40

Step-by-step explanation:

You have two sweatshirts that cost $30 more the day after.

First, you do [tex]340 -(2*30)[/tex]

Second, you divide what you got above ($280), by 7 and voila, you have $40 per sweatshirt.

Use the drawing tools to form the correct answer on the graph.
Every day the ocean has two low tides and two high tides. Function grepresents the height, in feet, of the water level in a cove relative to the
average sea level. Let trepresent the number of hours elapsed since the water height was equal to the average sea level after a low tide.
g(t) = 4sin(t)
Plot the points where g(t) is equal to the average sea level.

Answers

Answer:

The sinusoidal function that represent the height of the water level, is presented as follows;

[tex]g(t) = 4 \cdot sin \left(\dfrac{\pi}{6} \cdot t \right)[/tex]

Where;

t = The number of hours since the water height was the average sea level height

The graph of g(t) showing the points where g(t) = The average see level, created with MS Excel is attached

Step-by-step explanation:

Answer:

put a dot on points

(0,0)

(0,6)

(0,12)

Step-by-step explanation:

SOMEONE HELP ME PLEASE

Answers

Answer:

3/5 * 3/5 = 9/25 = .36 = 36%

Step-by-step explanation:

Which of the following statement is false?

a. all real numbers are complex numbers.

b. all irrational numbers are real numbers.

c. all complex numbers are pure imaginary numbers.

d. all whole numbers are rational numbers​

Answers

Answer:

c not all complex are imaginary

but all imaginary are complex

please brainlist

Answer:

C is False

Step-by-step explanation:

A complex number is represented by

[tex]z = a + bi[/tex]

A imaginary number is represented by

[tex]z = bi[/tex]

A complex number could include a real number so it cant be a pure imaginary number so C is False.

If triangle BCD was reflected over the x-axis, what would be the coordinates of the new triangle's vertices?
A. (-1, 0), (-1, -2), (-4, 1)
B. (-1, 0), (-1, 2), (-4, 1)
C. (-1, 0), (-1, 2), (4, -1)
D. (1, 0), (-1, 2), (-4, 1)

on time 4 learning

Answers

Answer:

b the answer is B because

Use elimination to solve the system 4x + 7y = –14 and 8x + 5y = 8 for x. Round to the nearest tenth.

Answers

Answer:

x = 3.5

y = - 4

Step-by-step explanation:

2(4x + 7y = -14)

8x + 14y = -28

  8x + 5y = 8

- (8x + 14y = -28)

--------------------------

        - 9y = 36

            y = 36/-9

            y = - 4

   4x + 7y = - 14

4x + 7(- 4) = - 14

     4x -28 = - 14

            4x = 14

              x = 14/4

              x = 3.5

Quadrilateral MNTU below is a parallelogram. If m2 M = 4x + 6 and m2N = 2x + 30, what is the value of x?

Answers

Answer:

x=12

Step-by-step explanation:

im not 100% but i think you would get the answer by setting the equations equal to one another.

4x+6=2x+30

2x=24

x=12

To the nearest degree, find the measure of angle A?

Answers

Answer:

I would say 26 or 42 but i would o with 26

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

[tex]arccos\left(\frac{18}{20}\right)[/tex] = 25.8

didn't pay attention and now im stuck :/

Answers

Answer:

A (First One)

Step-by-step explanation:

Side AC Is Congruent By Side DF

Side CB Is Congruent By Side FE

Side AB Is Congruent By Side DE

(There's no angles shown so it can't be the second option.)

The diagram has lines on the sides, if it we're SAS then the triangle would have an angle.

Answer:

ΔABC≅ΔDEF by SSS Postulate

Step-by-step explanation:

Hi there!

We are given 2 triangles

And we want to prove them congruent

You may notice that AC and FD have the same tick markings, AB and ED have the same tick markings, and CB and FE have the same tick markings

This means that those sides are congruent

In other words,

AC≅FD

AB≅DE

CB≅FE

If we have 3 pairs of congruent sides, that is enough for one concurrency postulate called side-side-side (SSS), which states that if 3 sides of a triangle are congruent to 3 sides in another triangle, then those triangles are congruent

So the triangles are congruent, but we need to put their vertices in the correct order

So if we make the name of the first triangle ABC, then we need to find the corresponding vertices in the second triangle

So let's find those vertices

D is corresponding to A, as they are both in between line segments that have 1 and 2 tick markings on them

E is corresponding to B, as they are both between line segments that have 2 and 3 tick markings on them

And finally, F is corresponding to C, as they are both between line segments that have 1 and 3 tick markings on them

So the name of the second triangle is DEF

ΔABC≅ΔDEF by SSS Posulate

Hope this helps!

can someone help with this, and explain it as well​

Answers

Answer:

WRS and VRT are vertical angles

Step-by-step explanation:

Vertical angles are formed by the same lines and share a vertex

WRS and VRT are vertical angles

Which one of the following sets is real numbers?

A. |x| = -1
B. |x| < -1
C. |x| > -1

Answers

The answer to your question is C

help asap answer ----------------

Answers

Answer:

[tex]f^-^1(f(3.14))=3.14[/tex]

[tex]f(f(-7))=5[/tex]

Step-by-step explanation:

Hi there!

[tex]f^-^1(f(x))=x[/tex]

Therefore,  [tex]f^-^1(f(3.14))=3.14[/tex]

[tex]f(f(-7))[/tex]

The table tells us that f(-7) is equal to -12.

[tex]f(-12)[/tex]

The table also tells us that f(-12) is equal to 5.

[tex]5[/tex]

I hope this helps!

For the following right triangle, find the side length x

Answers

Answer:

x = 25

Step-by-step explanation:

b² + h² = x²

24² + 7² = x²

576 + 49 = x²

625 = x²

√625 = √x²

25 = x

Step-by-step explanation:

x² = 7² + 24²

x² = 49 + 576

x² = 625

x = 25

10 times what equals 2204622621.8488?

Answers

Answer:

220462262.18488

Step-by-step explanation:

1. 2204622621.8488/10 = 220462262.18488

yea...we most def ain't learn this in class ​

Answers

Answer:

F. 300,000

Step-by-step explanation:

logically, it is decreasing by 1.

what is the solution to the system of equation below y=2/5x-3 and X=_10

Answers

Answer:

read explanation

Step-by-step explanation:

since y=2/5x-3 we substitute x=10 in making it y=2/5*10-3

following PAMDAS we do multiplication first so 2/5*10=4.

so y=4-3 and then we subtract and get y=1. Hope this helps:> if you need more explanation message me. If not give this a heart for helping. Good luck.

please help me with this problem !

Answers

Answer:
3/15
10/15

3 + 10 = 13

13/15


Multiply the numerator and the denominator of a fraction to the denominator of the other fraction.

Example:
The fraction 1/5
The denominator of the other fraction: 3
Multiply the numerator: 1*3 = 3
Multiply the denominator: 5*3 = 15

Combine: 3/15

Use the parabola tool to graph the quadratic function f(x)=−(x−2)2+4.

Answers

Answer:Use demos it could give you the answer

Step-by-step explanation:

the area of a rectangle is given by 6x²+19x+15. if x represents 4m, what are the dimensions of the length and width of the rectangle?​

Answers

Answer:

Length = 17m

Width = 11m

Step-by-step explanation:

Expression for the area of the rectangle = 6x² + 19x + 15

Factorising the quadratic expression

6x² + 19x + 15 = (6x² + 9x) + (10x + 15) = 3x(2x + 3) +5(2x + 3) = (3x + 5)(2x + 3)

x = 4m

Length = 3x + 5 = 3(4) + 5 = 12 + 5 = 17m

Width = 2x + 3 = 2(4) + 3 = 8 + 3 = 11m

During a sale, Cindy found boxes of dog biscuits on sale for $0.69 that had previously cost $2.23. What percentage is the discount?

Answers

Answer:

The dog biscuits are approximately 69% off.

Step-by-step explanation:

(1 - 0.69/2.23) * 100

(223/223 - 69/223) * 100

154/223 * 100 = 69%

Find x. PLEASE HELP ASAP

Answers

Answer:x=35.6

Step-by-step explanation:

look at the left triangle. I hope you're familiar with SOH, CAH and TOA.

sin 60°=O/(11√7)

so O= (11√7)sin 60°

now look at the triangle on the right.

cos 45=adjacent/x

cos 45=[(11√7)sin60°]/x

therefore, using ur calculator, you'll get x= [(11√7)sin60°]/cos 45

x=35.64407384

Suppose a normal distribution has a mean of 98 and a standard deviation of 6. What is P(x < 104)?
A. 0.16
B. 0.975
C. 0.84
D. 0.025

Answers

Answer:

Step-by-step explanation:

If the mean is 98, then 104 is only standard deviation away. If we are looking for the values less than this, we have the areas under the normal curve of 34%, 34%, 13.5%, 2.35%, .15% which add to 84%, or as a decimal, .84, choice C.

The z-score of the normal distribution P ( x ≤ 104 ) = 0.84

What is a z-score?

The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.

The Z-score is calculated using the formula:

z = (x - μ)/σ

where z: standard score

x: observed value

μ: mean of the sample

σ: standard deviation of the sample

Given data ,

Let the z-score of the distribution be z

And , the mean be μ = 98

And , the standard deviation be σ = 6

where z = (x - μ)/σ

So , P ( x ≤ 104 ) = [ P ( x - 98/6 ) ≤ 104 - 98 / 6 ) ]

On further simplification , we get

P ( x ≤ 104 ) = P ( x ≤ 1 )

Using a standard normal distribution table or calculator, we can find that the probability of a z-score less than 1 is approximately 0.8413. Therefore, the probability of x being less than 104 is approximately:

P(x < 104) = P(z < 1) ≈ 0.8413

So there is approximately an 84.13% chance that a value selected at random from this normal distribution will be less than 104

Hence , the probability is 0.84

To learn more about z-score click :

https://brainly.com/question/25638875

#SPJ7

Anyone know the answer? Pls help

Answers

the answer would be c

WILL GET BRAINLEST WILL HAVE TI ZOOM IN THI SHIW WORK TOO PLSSS ASAP

Answers

Answer:

sin = 1.333333

cos = 0.75

write the point-slope form of an equation of the line through the points (6,-1) and (5,7)

Answers

Answer:

y - 7 = -8 (x - 5)

Step-by-step explanation:

y2 - y1 / x2 - x1                7 - (-1) / 5 - 6           = -8

y - 7 = -8 (x - 5)


What is the multiplicative rate of change of the
exponential function shown on the graph?
81
2,
4
0
16
1
A
12
4
AN
8
1.
NI
-2.
2
-1.
9
x
(0,1)
1
-3 -2
-1
N
3

Answers

Answer:

The answer for thue would happened to be 2

-1.

Answer:

9/2

Step-by-step explanation:

Help Now Please!!!
Find The Volume Of This Cylinder

Answers

Answer:

502.4 m³.

Step-by-step explanation:

Formula: πr²h

4² = 16 x 10 = 160

160 x 3.14 (about π) ≈ 502.4 m³.

Hope this helps.

If there is something wrong, please let me know.

Answer:

160[tex]\pi[/tex] or

500[tex]m^{3}[/tex]

Step-by-step explanation:

[tex]\pi[/tex] x [tex]4^{2}[/tex] x 10 = 160[tex]\pi[/tex] or 500[tex]m^{3}[/tex]

56 out of the 56 employees at the sports shop are part-time employees. What percentage of the employees at the sports shop work part-time?

Answers

Answer:

100%

Step-by-step explanation:

Since 56/56 employees at the sports shop work part time, that means 100% of them do, or all of them.

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