A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
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)?
anonymous
 5 years ago
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)?

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0y=x ; \[\sin(.01)\approx.01\] \[\sin(.1)\approx.1\]\[\sin(1)\approx1\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0y=x ; \[\sin(.01)\approx.01\] \[\sin(.1)\approx.1\]\[\sin(1)\approx1\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Let'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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It 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 *

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The 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 \[\sin(x) \approx x.\]
Ask your own question
Sign UpFind more explanations on OpenStudy
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
 Engagement 19 Mad Hatter
 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.