Question

Find sin x/2, cos x/2, and tan x/2 from the given information.
cos x = −15/17, 180° < x < 270°

sin x/2=

cos x/2=

tan x/2=

Answer 1

\[2 \cos ^{2}\frac{ x }{ 2 }=1+\cos x=1-\frac{ 15 }{ 17 }=\frac{ 2 }{17 },\cos^{2}\frac{ x }{ 2 } =\frac{ 1 }{ 17 }\]
\[\cos \frac{ x }{ 2 }=-\frac{ 1 }{ \sqrt{17} } ....(1)\]
\[\sin \frac{ x }{ 2 }=\frac{ 1 }{ \sqrt{17} },90<\frac{ x }{ 2 }<135\]
\[\sin \frac{ x }{ 2 }>0,\cos \frac{ x }{ 2 }<0,\tan \frac{ x }{ 2 }<0\]
\[2\sin^{2}\frac{ x }{ 2 }=1-\cos x=1-\frac{ -15 }{ 17 }=\frac{ 32 }{ 17 },
\sin \frac{ x }{ 2 }=\frac{ 4 }{\sqrt{17} } .....(2)\]
divide (2) by (1) and get the value of tan x/2