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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
 one year ago
 one year 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
 one year ago
 one year ago

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myininayaBest ResponseYou've already chosen the best response.1
dw: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?
 one year ago

sunni0$UBest ResponseYou've already chosen the best response.0
I know them but I don't know how to use them.
 one year ago

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

sunni0$UBest ResponseYou've already chosen the best response.0
I know how to get the decimal answers, but I need exact answers.
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
Since 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
 one year ago

sunni0$UBest ResponseYou've already chosen the best response.0
For 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?
 one year ago

myininayaBest 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
 one year ago

sunni0$UBest ResponseYou've already chosen the best response.0
Ok thanks. I figured out the tan x/2 part
 one year ago
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