A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
Find sin x/2, cos x/2, and tan x/2, if cos x = 12/13, 180 degrees is less than x which is less than 270 degrees
anonymous
 3 years ago
Find sin x/2, cos x/2, and tan x/2, if cos x = 12/13, 180 degrees is less than x which is less than 270 degrees

This Question is Closed

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1352334915182:dw But anyways, mainly I drew this to show what quadrant we are in. sine and cosine are both negative in this quadrant Do you know the half angle identities for sine and cosine?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I know them but I don't know how to use them.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1\[\sin(\frac{x}{2})=\pm \sqrt{\frac{1}{2}(1\cos(x))}\] \[\cos(\frac{x}{2})=\pm \sqrt{\frac{1}{2}(1+\cos(x))}\] \[\tan(\frac{x}{2})=\frac{\sin(\frac{x}{2})}{\cos(\frac{x}{2})}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I know how to get the decimal answers, but I need exact answers.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1Since we are looking at the third quadrant and I said sine and cosine are both negative there, then we are actually looking at: \[\sin(\frac{x}{2})=\sqrt{\frac{1}{2}(1\cos(x))}\] \[\cos(\frac{x}{2})=\sqrt{\frac{1}{2}(1+\cos(x))}\] Replace cos(x) with what it equals which is 12/13 then simplify

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0For sin x/2 I got sqrt of 25/26, which is wrong apparently, but I got cos x/2=sqrt of 1/26 and it was right. Also, how do I find tan x/2 from all of this?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1\[\sin(\frac{x}{2})=\sqrt{\frac{1}{2}(1\frac{12}{13})} = \sqrt{\frac{1}{2}(1+\frac{12}{13})}=\sqrt{\frac{1}{2}(\frac{13}{13}+\frac{12}{13})}\] \[=\sqrt{\frac{1}{2}(\frac{25}{13})}=\sqrt{\frac{25}{26}}=\frac{\sqrt{25}}{\sqrt{26}}=\frac{5}{\sqrt{26}}\] This answer can be simplified more by choosing to rationalize the denominator

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Ok thanks. I figured out the tan x/2 part
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.