Need help on the Sin(4x) part of the question please!!

Need Help On The Sin(4x) Part Of The Question Please!!

Answers

Answer 1

a. The equivalent expression for cos(4x) in terms of just x is 8cos⁴x - 8cos²x + 1

b. The equivalent expression for sin(4x) in terms of just x is 4sinxcos³x - 2sinxcosx

a. The equivalent trigonometric expression for cos(4x)

To find the trigonometric expression for cos(4x)

cos(4x) = cos[2(2x)]

Now from trigonometric identities

cos2Ф = 2cos²Ф - 1

Let 2x = Ф.

So, cos(4x) = 2cos²2x - 1

Also, cos2x = 2cos²x - 1

So, substituting cos2x into cos4x, we have

cos(4x) = 2cos²2x - 1

cos(4x) = 2[2cos²x - 1]² - 1

cos(4x) = 2[4cos⁴x - 4cos²x + 1] - 1

cos(4x) = 8cos⁴x - 8cos²x + 2 - 1

cos(4x) = 8cos⁴x - 8cos²x + 1

So, the equivalent expression for cos(4x) in terms of just x is 8cos⁴x - 8cos²x + 1

b. The equivalent trigonometric expression for sin(4x)

To find the expression for sin(4x)

sin(4x) = sin2(2x)

From trigonometric identities sin2Ф = 2sinФcosФ

Let 2x = Ф

So, sin(4x) = sin2(2x)

= 2sin2xcos2x

Since

sin2x = 2sinxcosx and cos2x = 2cos²x - 1

Substituting these into the equation, we have

sin(4x) =  2sin2xcos2x

sin(4x) = (2sinxcosx)(2cos²x - 1)

sin(4x) = 4sinxcos³x - 2sinxcosx

So, the equivalent expression for sin(4x) in terms of just x is 4sinxcos³x - 2sinxcosx

Learn more about trigonometric expression here:

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Related Questions

Round 259.98991 to the nearest hundredth.
259.99
259.990
259.9899
260.00001

Answers

259.99

HTU.TH

(hundreds, tens, units . tenths, hundredths)


The senior classes at High School A and High School B planned separate
trips to the state fair. The senior class at High School A rented and filled 3
vans and 13 buses with 628 students. High School B rented and filled 9
vans and 2 buses with 182 students. Every van had the same number of
students in it as did the buses. Find the number of students in each van
and in each bus. *
Van: 10, Bus: 46
Van: 15, Bus: 70
Van: 4, Bus: 22
Van: 46, Bus: 10

Answers

Answer: Van: 10, Bus: 46

Step-by-step explanation:

Let the number of students in each van be represented by v.

Let the number of students in each bus be represented by b.

The question given can be formed into an equation as:

3v + 13b = 628 ...... i

9v + 2b = 182 ......... ii

Multply equation i by 9

Multiply equation ii by 3

27v + 117b = 5652 ........ iii

27v + 6b = 546 ....... iv

Subtract iv from iii

111b = 5106

b = 5106/111

b = 46

Bus = 46

Recall that 9v + 2b = 182

9v + 2(46) = 182

9v + 92 = 182

9v = 182 - 92

9v = 90

v = 90/9

v = 10

Van = 10

Describe the differences in the graphs of linear functions vs. exponential functions.

A. Linear functions have a constant slope, while exponential functions start flat and get steeper.

B. Linear functions cross the y-axis above exponential functions.

C. Linear functions slope down, while exponential functions slope up.

D. There is no
differhoice.

I’ll give brainiest

Answers

Answer:

It's A.

(Just finished the quiz) <3

The differences in the graphs of linear functions vs. exponential functions

is, A. Linear functions have a constant slope, while exponential functions start flat and get steeper.

What is a linear equation?

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

A function is an exponential function when the exponent is the variable.

The difference between a linear function and an exponential function is,

while exponential functions begin flat and gradually steepen, linear functions have a constant slope.

learn more about exponential functions here :

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Use distributive property to rewrite each algebraic expression: 8(s + 5)

Answers

Answer:

8s + 40

Step-by-step explanation:

8*s = 8s

8*s = 40

8s + 40

Answer: The correct answer is 8s+40

Step-by-step explanation: If it's correct can i get brainliest..... hopes this helps.

SOMEONE PLEASE HELP ME AND ANSWER THIS QUESTION CORRECTLY I WILL MAKE YOU THE BRAINLIEST, GIVE YOU A GOOD RATE, PLEASE ASWER THIS ASAPPPPPPPPP!!!!!!!!!!! I NEED HELP ASAPPPPPPPPPPP!!!!!!!!!! ALSO PLEASE SHOW YOUR WORK ASAPPPPPPP!!!!!!!!!!!!

Answers

Answer:

tbh that doesnt make sense the easiest way to et the first one is to do 955 divided by 90.

Step-by-step explanation:

The frequency, f, in Hz, at which a simple pendulum rocks back and forth is given by 1 , 2 g f π l = where g is the strength of the gravitational field at the location of the pendulum, and l is the length of the pendulum. a. Find the frequency of a pendulum whose length is 1 foot and where the gravitational field is approximately 32 ft/s2 b. The strength of the gravitational field on the moon is about 1 6 as strong as on Earth. Find the frequency of the same pendulum on the moon.

Answers

Answer:

a. 0.9 Hz b. 0.37 Hz

Step-by-step explanation:

The frequency of the simple pendulum f = (1/2π)√g/l where g = acceleration due to gravity and l = length of pendulum

a. Find the frequency of a pendulum whose length is 1 foot and where the gravitational field is approximately 32 ft/s2

To find f on Earth, g = 32 ft/s² and l = 1 ft

So, f =  (1/2π)√(g/l)

f = (1/2π)√(32 ft/s²/1 ft)

f = (1/2π)√(32/s²)

f = (1/2π)(5.66 Hz)

f = 0.9 Hz

b. The strength of the gravitational field on the moon is about 1/6 as strong as on Earth.. Find the frequency of the same pendulum on the moon.

On the moon when acceleration due to gravity g' = g/6,

f =  (1/2π)√(g'/l)

f =  (1/2π)√(g/6l)

f = (1/2π)√[32 ft/s²/(6 × 1 ft)]

f = (1/2π)√(32/s²)/√6

f = (1/2π)(5.66 Hz)/√6

f = 0.9/√6 Hz

f = 0.37 Hz

The temperature was -5 degrees and then fell 8 degrees. What is the temperature now?

Answers

Answer:

-13 degrees tell me if it's right

Answer:

-13 is the answer

Step-by-step explanation:

because -5-8= -13

Find the Values of x and y

Answers

the answer is x = 2 and y = 17

Fifteen disks with the given measurements are stacked on top of each other. Which expression does NOT give the volume of the cylinder that is formed?

Answers

Missing information:

[tex]r = 3cm[/tex]

[tex]h = 1cm[/tex]

Options:

(a) [tex]\pi * 3^2 * 15[/tex]          (b) [tex]\pi * 3* 15^2[/tex]

(c) 15 times the volume of the disk

(d) The height of the stack multiplied by [tex]\pi r^2[/tex]

Answer:

(b) [tex]\pi * 3* 15^2[/tex]

Step-by-step explanation:

Given

15 identical disks

[tex]r = 3cm[/tex]

[tex]h = 1cm[/tex]

Required

Determine the odd option

The volume of 1 disk is:

[tex]V_1 = \pi r^2h[/tex]

[tex]V_1 = \pi * 3^2 * 1[/tex]

The volume of 15 is:

[tex]V_{15} = 15 * V_1[/tex]

[tex]V_{15} = 15 * \pi * 3^2 * 1[/tex]

[tex]V_{15} = \pi * 3^2 * 15[/tex]

The above equation represents (a), (c) and (d)

Because:

(a):  [tex]V_{15} = \pi * 3^2 * 15[/tex]

(c) 15 * volume of the disk: [tex]V_{15} = 15 * V_1[/tex] = [tex]V_{15} = \pi * 3^2 * 15[/tex]

(d) height * [tex]\pi r^2[/tex] = h * [tex]\pi r^2[/tex] = [tex]15 * \pi * 3^2 * 1[/tex] = [tex]V_{15} = \pi * 3^2 * 15[/tex]

Hence, (b) is the odd option

Which of the following is a diameter of Circle O?
A
AB
B
DG
EB
D
AE

Answers

Answer:

EB

Step-by-step explanation:

Diameter is a line that cut a circle into equal halves

O indicate the point of the center

Answer the photo below thanks

Answers

Answer: rotation

Step-by-step explanation:

Find the value of x for brainliest

Answers

Answer:

x=27.5

Step-by-step explanation:

x/4=55/8

Cross multiply:

8x=220

Divide:

8x/8=220/8

x=27.5

How Many Miles please help me.

Answers

10.5 i think if not sorry

Brandon buys a radio for $43.75 in a state where the sales tax is 7%.


Part 1 out of 2
How much does he pay in taxes? If necessary, round to the nearest cent

Answers

Answer:

Tax: $3.06

Step-by-step explanation:

7% of 43.75 = 0.07 × 43.75 = 3.0625

43.75 increase 7% =

43.75 × (1 + 7%) = 43.75 × (1 + 0.07) = 46.8125

Radio: $43.75

Tax: $3.06

Total: $46.81

does anyone know the answer to 5(2t+3)=75 that can tell me how to find the answer not just the answer

Answers

Answer: Let me know if this helps.

Step-by-step explanation:

5(2t+3)=75     Distribute the 5 using multiplication. 5x2t and 5x3

10t+15=75      Subtract 15 because you need to get the t by itself.

10t = 60         Now divide by 10 to get t by itself. 10/10 and 60/10.

t = 6               Answer.

Answer:

t=6

Step-by-step explanation:

It's all about get t on one side of the equation, and so everything else on the other side of the equation.

The first thing we want to get rid of is the 5. The 5 is multiplied by (2t+3), so to get rid of it, we divide both sides by five (divide both sides since they must remain equal):

(5(2t+3))/5=75/5

2t+3=15

The next thing we can get rid of is the 3. Subtract 3 from both sides:

2t+3-3=15-3

2t=12

Now, we get rid of the 2. Divide both sides by 2:

2t/2=12/2

t=6

Solve for x
Solve for x

Answers

Answer:

23.1

Step-by-step explanation:

14/20*x/33

Cross multiply

14*33=20*x

462=20*x

462/20=x

23.1=x

Hope this helps :)

Answer:

According to the ratio of segments:-

[tex]\frac{20}{14} =\frac{33}{x}[/tex]

[tex]20x=14(33)[/tex]

[tex]20x=462[/tex]

[tex]x=\frac{462}{20}[/tex][tex]=23.1[/tex]------------------------hope it helps...have a great day!!

The measure of angle 1 is 130°.
2 lines intersect to form 4 angles. From top left, clockwise, the angles are 1, 4, 3, 2.
Which other angle must also measure 130°?

Answers

Answer:

The angle opposite angle 1

Step-by-step explanation:

Opposite angles have the same degree when two lines intersect because they are vertical angles.

Answer:

3

Step-by-step explanation:

Are the two expressions in the equation 2b + 5 + 1b = 3b + 5 equal or equivalent? How do you know?

Answers

Answer:

they are equal because while solving 2b+5+1b it will come 3b+5 so they are equal

Answer:

the equation are equivalent

Step-by-step explanation:

to know why, look at the pic above

Determine the sine, cosine, and tangent of angle THETA. Check tje appropriate solution for each.​

Answers

Step-by-step explanation:

c²=a²+b²

a²=c²-b²

a²= 15²-9²=225-81=144

a=√144=12

sinΩ=a/c=12/15=4/5

cosΩ=b/c=9/15=3/5

tanΩ=a/b=12/9=4/3

Donna paid $3 to rent shoes and then $1 for each game she played at a bowling alley. She spent a total of $8 at the bowling alley.

Which equation can be used to find the number of games Donna played?

Answers

Answer:If shoes are for all games in row,  P = 2 + 3 g   If not,  P = 5 g  ,with g the number of games

Explanation: The price depends:if shoes are included for the whole games, you just have to pay them once and then you have to pay  

g g a m e s , so  P ( g ) = 2 + 3 g   Else, you have to pay  g s h o e s  and  g b o w l p a r t y ,so  

P ( g ) = 2g + 3 g⇔ P ( g ) = 5 g

Hope this helped hope you get a good score on your assignment/test/quiz/homework

-Tay did this

find the unknown Angles in the given figure

Answers

Answer:

x = 50°, y = 50°

Step-by-step explanation:

⇒ x + x + 80° = 180°

⇒ 2x = 180° - 80° = 100°

⇒ x = 100°/2 = 50° ∴ y = x = 50°

How to change a decimal into a fraction? Specific question: change 1.25 to an exact percent?

Answers

Answer:

125%

Step-by-step explanation:

1.25 x 100% = 125%

Find the missing side of each right triangle. Side c is the hypotenuse. Sides a and b are the legs. Leave your answers in simplest radical form.

A=11m,C=15m

Find b with writing it out like the picture above.

Answers

Answer:

Side b = 10.2 m (1 d.p.)

Step-by-step explanation:

11² = 121

15² = 225

225 - 121 = 104

√104 = 10.2 (1 d.p.)  

Side b = 10.2m

(Full answer = 10.198039)

11² + 10.2² = 15²

Linear Equations & Linear Systems:Question 5
What is the solution to the following system of equations?

Somebody pls help me

Answers

(2, -3) is the solution

so it said to pick which statement is true about the measurements of angles ABC. so I said B, can someone check if this is correct please ​

Answers

Answer:

Its c.

Step-by-step explanation:

Because B is the smallest point on that picture.

BrainliesT?

Answer:

your answer is correct

Step-by-step explanation:

have A great day

Helppppppppppppppppp

Answers

Answer:

The answer will be 24

Step-by-step explanation:

Hope this Helped

Answer:

24

Step-by-step explanation:

Graph the equation y= 5x - 4

Answers

Answer:

the y intercept will be -4 and the slope would be 5

what form is the equation 12y=2x=24

Answers

Answer:

Step-by-step explanation:

Simplifying

12y + 2x = 24

Reorder the terms:

2x + 12y = 24

Solving

2x + 12y = 24

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-12y' to each side of the equation.

2x + 12y + -12y = 24 + -12y

Combine like terms: 12y + -12y = 0

2x + 0 = 24 + -12y

2x = 24 + -12y

Divide each side by '2'.

x = 12 + -6y

Simplifying

x = 12 + -6y

SMART PPL HELP HELP PLEAse

Answers

Answer:

help with what

Step-by-step explanation:

Answer:

did you mean to post a question?

Step-by-step explanation:

7x + 2y = 24
8x + 2y = 30

Answers

Answer:

x=6

so

6x7

42+ = 24/2

12-42

y=-30

Step-by-step explanation:

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