1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sweet-ann [11.9K]
3 years ago
10

PLEASE HELP I DO NOT UNDERSTAND AT ALL ITS PRECALC PLEASE SERIOUS ANSWERS

Mathematics
2 answers:
Elina [12.6K]3 years ago
8 0

You want to end up with A\sin(\omega t+\phi). Expand this using the angle sum identity for sine:

A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi

We want this to line up with 2\sin(4\pi t)+5\cos(4\pi t). Right away, we know \omega=4\pi.

We also need to have

\begin{cases}A\cos\phi=2\\A\sin\phi=5\end{cases}

Recall that \sin^2x+\cos^2x=1 for all x; this means

(A\cos\phi)^2+(A\sin\phi)^2=2^2+5^2\implies A^2=29\implies A=\sqrt{29}

Then

\begin{cases}\cos\phi=\frac2{\sqrt{29}}\\\sin\phi=\frac5{\sqrt{29}}\end{cases}\implies\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)

So we end up with

2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)

Leni [432]3 years ago
5 0

Answer:

  • y(t) = √29·sin(4πt +1.1903)
  • amplitude: √29
  • angular frequency: 4π
  • phase shift: 1.1903 radians

Step-by-step explanation:

In the form ...

  y(t) = Asin(ωt +φ)

you have ...

  • Amplitude = A
  • angular frequency = ω
  • phase shift = φ

The translation from ...

  y(t) = 2sin(4πt) +5cos(4πt)

is ...

  A = √(2² +5²) = √29 . . . . the amplitude

  ω = 4π . . . . the angular frequency in radians per second

  φ = arctan(5/2) ≈ 1.1903 . . . . radians phase shift

Then, ...

  y(t) = √29·sin(4πt +1.1903)

_____

<em>Comment on the conversion</em>

You will notice we used "2" and "5" to find the amplitude and phase shift. In the generic case, these are "coefficient of sin( )" and "coefficient of cos( )". When determining phase shift, pay attention to whether your calculator is giving you degrees or radians. (Set the mode to what you want.)

If you have a negative coefficient for sin( ), you will need to add 180° (π radians) to the phase shift value given by the arctan( ) function.

You might be interested in
Please answer please
Murrr4er [49]

<BAC = <DEC = 30°

<BCA = <DCE = 70°

<CDE (or m<D) = 180° - <DEC - <DCE

<CDE = 180° - 30° - 70°

<CDE = 80°

The number that belongs in the green box is 80

3 0
3 years ago
Help please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11
pogonyaev
Answer is A: when you add all the percents it’s 50 the rest is 50%
3 0
3 years ago
Read 2 more answers
2+3+7+34+7000+12242534
sashaice [31]

Answer:

The answer is 12249580

Step-by-step explanation:

add all the numbers:)

4 0
3 years ago
Read 2 more answers
Which of these steps will eliminate a variable in this system?
PSYCHO15rus [73]
C. multiply the second equation by two. Then add the equations
3 0
3 years ago
I need to find the area of the shaded region, but I need detailed steps
olasank [31]
The shaded region is a parallelogram.

The formula for the area of any parallelogram is A=bh.

The base of the parallelogram is 2 meters long (given).

The height of the parallelogram is 9 meters (do not be fooled by the unnecessary information of 14 meters)
The height is 9 meters because the height has to be perpendicular to the base. Thus, the side length must be 9 meters.

Multiply them together.

2 \times 9 = 18

The area of the parallelogram is 18 square meters.
7 0
3 years ago
Other questions:
  • I need help with these 3 problems
    15·1 answer
  • Which of the following relation is correct
    7·1 answer
  • What is the best estimate of the mean price of all the sunglasses on the rack?
    7·2 answers
  • Hannah went swimming after she woke up. It took Hannah 15 minutes to get ready to go swimming. She swam for 30 minutes and then
    11·1 answer
  • Mr. Thompson needs to move two large boxes of toys from the store to his house. The first box measures 6 ft long × 4 ft tall × 5
    5·1 answer
  • Need help fastt plss will give brainliest too who is corect plssss helppp
    10·2 answers
  • What is the volume of the pyramid? <br> DO NOT ROUND UR NUMBER!!!
    14·2 answers
  • What is the critical value t* which satisfies the condition that the t distribution with 14 degrees of freedom has probability 0
    10·1 answer
  • How do you find the slope of a line on a graph?
    10·2 answers
  • Based on the information in the diagram, can you prove that the figure is a parallelogram explain
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!