Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

dpflan Group Title

What is the linear approximation for sin(x) at x=0? How can I use the answer the approximate the values of sin(.01), sin(.1) and sin(1)?

  • 3 years ago
  • 3 years ago

  • This Question is Closed
  1. JoanLu Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    y=x ; \[\sin(.01)\approx.01\] \[\sin(.1)\approx.1\]\[\sin(1)\approx1\]

    • 3 years ago
  2. JoanLu Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    y=x ; \[\sin(.01)\approx.01\] \[\sin(.1)\approx.1\]\[\sin(1)\approx1\]

    • 3 years ago
  3. kh83 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Let's see sin(0.01) = 0.00999, relative error = 0.002%, very good sin(0.1) = 0.099, error 0.1% that's good sin(1) = 0.8415, error = 16 % - that's unacceptable but 1 radian is pretty big angle

    • 3 years ago
  4. l Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    It depends on what type of equation/formulation you are using. For example if y = 1/sin(x). There's a great difference between sin0, sin0.1 and sin 1. As a numerical analysis method you can look up Newton's Approximation Formula: http://en.wikipedia.org/wiki/Newton's_method *

    • 3 years ago
  5. hburgiel Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    The linear approximation for sin(x) at x=0 is just the equation of the tangent line to the graph of sin(x) at x=0. So \[\sin(x) \approx x.\]

    • 3 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.