Question

Use the given information to find exact answers for cos(x/2), sin(x/2), and tan(x/2):
Cos (x)=-4/5
180 degrees< x < 270 degrees

Answer 1

\[2 \sin ^2 \frac{ x }{ 2 }=1-\cos x\]
\[2 \cos ^2\frac{ x }{ 2 }=1+\cos x\]
\[180<x<270,90<\frac{ x }{ 2 }<135\]
\[\frac{ x }{ 2 }~lies~\in~second~quadrant.\]
\[\sin \frac{ x }{ 2 }~is~positive.\]
\[\cos \frac{ x }{ 2 }~is~negative.\]
\[\tan \frac{ x }{ 2 }~is~negative.\]
\[\tan \frac{ x }{ 2 }=\frac{ \sin \frac{ x }{ 2 } }{ \cos \frac{ x }{ 2 } }\]