A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

show that eq has atleast one root in the given interval cos2x+sinx=0 , [-pi/2,pi/2]

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1-2sin^2x+sinx=0 2sin^2x-sinx-1=0 2sinx(sinx-1) +1(sinx-1)=0 sinx=1 or sinx=-1/2 x=pi/2 or x=-pi/6

  2. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    cos(2x) + sin(x) = 0 cos(2x) = sin(-x) cos^2 - sin^2 +sin(x) = 0 (1 - sin^2) +sin^2 + sin(x) = 0 1+sin(x) = 0 sin(x) = -1 x = -pi/2

  3. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ack!!!....

  4. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    really need to do these on paper ;)

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[cos(-\pi) = -1\] \[sin (-\pi/2) = -1\] \[cos(\pi) = -1\] \[sin(\pi/2) = 1\] So at least it will be 0 at \(\pi/2\). Another easy way would be if you found a positive and a negative then the intermediate value theorem would tell you you had a root somewhere in there.

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It doesn't specifically ask you to find it

  7. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.