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
Dominik [7]
3 years ago
10

The following two sets of parametric functions both represent the same ellipse. Explain the difference between the graphs.

Mathematics
2 answers:
statuscvo [17]3 years ago
7 0
The answer
ellipse main equatin is as follow:

X²/ a²   +  Y²/ b²  =1, where a≠0 and b≠0

for the first equation: <span>x = 3 cos t and y = 8 sin t
</span>we can write <span>x² = 3² cos² t and y² = 8² sin² t
and then  </span>x² /3²= cos² t and y²/8² =  sin² t
therefore,  x² /3²+ y²/8²  =  cos² t + sin² t = 1
equivalent to x² /3²+ y²/8²  = 1

for the second equation, <span>x = 3 cos 4t and y = 8 sin 4t we found
</span>x² /3²+ y²/8²  = cos² 4t + sin² 4t=1

ehidna [41]3 years ago
7 0

Answer with explanation:

The two parametric equation of the same ellipse is

x = 3 cos t and y = 8 sin t

x = 3 cos 4 t and y = 8 sin 4 t

\frac{x}{3}=\cos t\\\\ \frac{x}{3}=\cos 4t\\\\ \frac{y}{8}=\sin t\\\\ \frac{y}{8}=\sin 4t\\\\ (\frac{x}{3})^2+ (\frac{y}{8})^2=\sin^2t+\cos^2t \text{or}=\sin^2 4t+\cos^2 4t=1\\\\\frac{x^2}{9}+\frac{y^2}{64}=1

This is the equation of same ellipse, having different Parametric forms.

→The function involving , 3 cos t and 8 sin t has maximum value, 3 and 8,respectively , and a period of π  , whereas, the function  3 cos 4 t and , 8 sin 4 t , has also same maximum value, 3 and 8,respectively , but period changes , the period after which cycle of trigonometric function  sin 4 t and cos 4 t  repeats is, t=\frac{\pi}{4}.

→x = 3 cos t and y = 8 sin t

\frac{x}{y}=\frac{3}{8 \tan t}\\\\y=\frac{8 \tan t*x}{3}

→x = 3 cos 4 t and y = 8 sin 4 t

\frac{x}{y}=\frac{3}{8 \tan 4 t}\\\\y=\frac{8 \tan 4 t*x}{3}

Also, these are equation of two lines having different slopes both passing through the origin.

You might be interested in
Marcus looked out in the audience and saw 40% of the chairs were filled. There were 42 people sitting in the chairs. Enter the t
puteri [66]

Answer:

I say it is 16.8

Step-by-step explanation:

40 x 42

100

= 16.8

4 0
2 years ago
Help me out, thanks.
fiasKO [112]
30x^3 10x
i’m sorry if that doesn’t help but it works out right to me
have a good day hun xox
5 0
3 years ago
Read 2 more answers
In the band, there are 2 vocalists and 5 musicians. What is the ratio of musicians to vocalists
AfilCa [17]

Answer:

The answer is D. 5 to 2

Step-by-step explanation:

It sounds like they want the ratio to be given in that order.

Hope that helps!

3 0
2 years ago
Write an equation of the circle with center (3,-2) and radius 6
Lubov Fominskaja [6]

Answer:

\displaystyle (x-3)^2 + (y+2)^2 = 36

Step-by-step explanation:

We want to write the equation of a circle with a center at (3, -2) and a radius of 6 units.

Recall that the equation of a circle is given by:

\displaystyle (x-h)^2 + (y-k)^2 = r^2

Where (<em>h, k</em>) is the center and <em>r</em> is the radius.

Since our center is at (3, -2), <em>h</em> = 3 and <em>k</em> = -2. <em>r</em> = 6. Substitute:

\displaystyle (x-(3))^2  +(y-(-2))^2 = (6)^2

Simplify:

\displaystyle (x-3)^2 + (y+2)^2 = 36

In conclusion, the equation of the circle will be:

\displaystyle (x-3)^2 + (y+2)^2 = 36

8 0
2 years ago
According to the lesson, a decimal number is defined as which of the following?
matrenka [14]

A decimal is the dot that separates the whole numbers from the numbers LESS THAN one.

Answer=A

-Steel jelly


7 0
2 years ago
Other questions:
  • Randall invests $7200 in two different accounts. The first account paid 11 %, the second account paid 13 % in interest. At the e
    15·1 answer
  • Can someone plz help me with this?
    8·1 answer
  • A rope from the top of a mast on a sailboat is attached to a point 6 feet from the base of the mast. If the rope is 24 feet long
    15·1 answer
  • Given that f(x) = 2x −5, find the value of x that makes f(x) = 15. (5 points)
    13·2 answers
  • Definition of Inquality
    13·2 answers
  • Help I will be marking brainliest!! No links please!
    15·2 answers
  • How many ways are there to place 3 indistinguishable red chips, 3 indistinguishable blue chips, and 3 indistinguishable green ch
    6·1 answer
  • The figure below shows a line graph and two shaded triangles that are similar: Which statement about the slope of the line is tr
    12·2 answers
  • I need the answer in the next 6 hours
    14·2 answers
  • Last week, Riley worked 7.5 hours per day for 3 days and earned a total of $306.45.
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!