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

glucy7 Group Title

Find the exact value by using a half-angle identity. tan7π/8 PLEASE PLEASE PLEASE :)

  • one year ago
  • one year ago

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

    Well, the half angle identity says: \[ \sin(\theta/2) = \sqrt{\frac{1-\cos(\theta)}{2}} \quad \cos(\theta/2) = \sqrt{\frac{1+\cos(\theta)}{2}} \]

    • one year ago
  2. glucy7 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    but what about tan..

    • one year ago
  3. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Well \[ \tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)} \]So I didn't really remember it's identity for this. Rather, I just divided the other identities.

    • one year ago
  4. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    So then \[ \tan(\theta / 2) = \sqrt{\frac{1-\cos(\theta)}{1+\cos(\theta)}} \]

    • one year ago
  5. glucy7 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    well i just don't really understand how to do the problem once everything is plugged in

    • one year ago
  6. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, \(\cos(7\pi/4)\) is relatively easy to solve for, when you look at the unit circle.

    • one year ago
  7. glucy7 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    well i know how to find the degree but once i get the degree i dont know where to go from there

    • one year ago
  8. Rosh007 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    that is a good method... but tan's identity is below \[\large \tan (\frac{ \theta }{ 2 }) =\frac{ \sin(\theta) }{1+ \cos (\theta) }=\frac{ 1- \cos (\theta) }{\sin(\theta) }\]

    • one year ago
  9. glucy7 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    do you mind just showing me the steps please??

    • one year ago
  10. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1353034351647:dw|

    • one year ago
  11. glucy7 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    can you use the half angle formula

    • one year ago
  12. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, if you consider 7pi/8 to be a half angle, then that means the full angle is 7pi/4

    • one year ago
  13. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Since for 7pi/4 it is easy to find the values of sin/cos, it is useful here.

    • one year ago
  14. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Think of it this way, 7pi/4 is pi/4 short of 2pi. 2pi is a full circle. So pi/4 is just a quarter of a circle.

    • one year ago
  15. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    What makes a quarter of a circle easy to calculate, is the fact that the you know the the horizontal and vertical part are equal, so I set them to a and solved for a to find the value of cos

    • one year ago
  16. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \(a^2+a^2=1\) is just Pythagorean theorem.

    • one year 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.