Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

glucy7

  • 2 years ago

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

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

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

  2. glucy7
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but what about tan..

  3. wio
    • 2 years ago
    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.

  4. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  5. glucy7
    • 2 years ago
    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

  6. wio
    • 2 years ago
    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.

  7. glucy7
    • 2 years ago
    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

  8. Rosh007
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  9. glucy7
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do you mind just showing me the steps please??

  10. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1353034351647:dw|

  11. glucy7
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can you use the half angle formula

  12. wio
    • 2 years ago
    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

  13. wio
    • 2 years ago
    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.

  14. wio
    • 2 years ago
    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.

  15. wio
    • 2 years ago
    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

  16. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

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

    • Attachments:

Ask your own question

Ask a Question
Find 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
  • 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.