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
patriot [66]
3 years ago
6

The curve given by x=sin(t),y=sin(t+sin(t)) has two tangent lines at the point (x,y)=(0,0). List both of them in order of increa

sing slope. Your answers should be in the form of y=f(x) without t′s.
Mathematics
1 answer:
SOVA2 [1]3 years ago
5 0

Answer:

y = 0

y =2x

Step-by-step explanation:

Given parametric equations:

x (t) = sin (t)

y (t) = sin (t + sin (t))

The slope of the curve at any given point is given by dy / dx we will use chain rule to find dy / dx

(dy / dx) * (dx / dt) = (dy / dt)

(dy / dx) = (dy / dt) / (dx / dt)

Evaluate dx / dt and dy / dt

dx / dt = cos (t)

dy / dt = cos (t + sin (t)) * (1+cos (t))

Hence,

dy / dx = (1+cos(t))*cos(t + sin (t))) / cos (t)

@Given point (x,y) = 0 we evaluate t

0 = sin (t)

t = 0 , pi

Input two values of t and compute dy / dx

@ t = 0

dy / dx = (1 + cos (0))*cos (0 + sin (0))) / cos (0)

dy / dx = (1+1)*(1) / (1) = 2 @ t = 0

@t = pi

dy / dx = ( 1 + cos (pi))* cos (pi + sin (pi)) / cos (pi)

dy / dx = (1-1) * (-1) / (-1) = 0 @ t = pi

The corresponding gradients are 0 and 2 in increasing order and their respective equations are:

y = 2x

y = 0

You might be interested in
8/9 + 4/7 =<br> Can you get the Anwar for this sum
attashe74 [19]

here. I don't know if its right but i hope it is.

7 0
3 years ago
Read 2 more answers
4. A light bulb was being tested so it was left on
PolarNik [594]

Answer:

696 hours

Step-by-step explanation:

8 0
2 years ago
I had a dream of a beautiful cupcake tree, growing 4 loveee cupcakes every 12 hours for 36 hours. Please make my dream come true
weqwewe [10]

Answer: sounds sweet:)

Step-by-step explanation:

7 0
3 years ago
Please help! 12 points
Ivahew [28]

Answer:

Step-by-step explanation:

sin2x = 2sinx*cosx

         = 2\sqrt{sin^{2}x } * cosx

         = 2\sqrt{(1-cos^{2}x } * cosx

         = 2  \sqrt{1-\frac{3}{5} ^{2} } *\frac{3}{5}

         = \frac{8}{5}  * \frac{3}{5}  

         = 24/25        

8 0
3 years ago
NEED HELP ASAP!!!! Due by 4!!!! The question is the triangle find x
sashaice [31]
It’s 15x plus 1 I believe it is the sender
5 0
3 years ago
Other questions:
  • 1 point
    11·1 answer
  • The ratio of long boards to short boards is 4 to
    10·2 answers
  • WILL MARK YOU BRAINLIEST !!!
    6·1 answer
  • If you can help please do :)
    5·1 answer
  • Help please really need
    6·1 answer
  • Use the laws of Sines and law of cosines to find missing Dimensions. Part 2​
    13·2 answers
  • How does the order of the numbers affect the product in multiplication problems
    7·1 answer
  • What value of c make the relation (c,9), (8,7),(6,5) a function
    14·1 answer
  • Determine the equation of a circle with its centre at the origin in the Cartesian plane and with a radius of 2√3 units​
    13·1 answer
  • Use 3.14 for pi. ROUND YOUR FINAL ANSWER TO THE NEAREST TENTHS PLACE!
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!