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anonymous
 4 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
 4 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

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myininaya
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.0I know them but I don't know how to use them.

myininaya
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.0I know how to get the decimal answers, but I need exact answers.

myininaya
 4 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
 4 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
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.0Ok thanks. I figured out the tan x/2 part
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