A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
Find the exact value by using a halfangle identity.
tan7π/8
PLEASE PLEASE PLEASE :)
 2 years ago
Find the exact value by using a halfangle identity. tan7π/8 PLEASE PLEASE PLEASE :)

This Question is Closed

wio
 2 years ago
Best ResponseYou've already chosen the best response.1Well, the half angle identity says: \[ \sin(\theta/2) = \sqrt{\frac{1\cos(\theta)}{2}} \quad \cos(\theta/2) = \sqrt{\frac{1+\cos(\theta)}{2}} \]

wio
 2 years ago
Best ResponseYou've already chosen the best response.1Well \[ \tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)} \]So I didn't really remember it's identity for this. Rather, I just divided the other identities.

wio
 2 years ago
Best ResponseYou've already chosen the best response.1So then \[ \tan(\theta / 2) = \sqrt{\frac{1\cos(\theta)}{1+\cos(\theta)}} \]

glucy7
 2 years ago
Best ResponseYou've already chosen the best response.0well i just don't really understand how to do the problem once everything is plugged in

wio
 2 years ago
Best ResponseYou've already chosen the best response.1Well, \(\cos(7\pi/4)\) is relatively easy to solve for, when you look at the unit circle.

glucy7
 2 years ago
Best ResponseYou've already chosen the best response.0well i know how to find the degree but once i get the degree i dont know where to go from there

Rosh007
 2 years ago
Best ResponseYou've already chosen the best response.0that is a good method... but tan's identity is below \[\large \tan (\frac{ \theta }{ 2 }) =\frac{ \sin(\theta) }{1+ \cos (\theta) }=\frac{ 1 \cos (\theta) }{\sin(\theta) }\]

glucy7
 2 years ago
Best ResponseYou've already chosen the best response.0do you mind just showing me the steps please??

glucy7
 2 years ago
Best ResponseYou've already chosen the best response.0can you use the half angle formula

wio
 2 years ago
Best ResponseYou've already chosen the best response.1yes, if you consider 7pi/8 to be a half angle, then that means the full angle is 7pi/4

wio
 2 years ago
Best ResponseYou've already chosen the best response.1Since for 7pi/4 it is easy to find the values of sin/cos, it is useful here.

wio
 2 years ago
Best ResponseYou've already chosen the best response.1Think 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.

wio
 2 years ago
Best ResponseYou've already chosen the best response.1What 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

wio
 2 years ago
Best ResponseYou've already chosen the best response.1\(a^2+a^2=1\) is just Pythagorean theorem.
Ask your own question
Ask a QuestionFind 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.