Question
Find sin x/2, cos x/2, and tan x/2 from the given information. (show work please) thank you!!!
cos x = − 4/5, 180° < x < 270°
cos x = − 4/5, 180° < x < 270°
Answers
Reiny
so the angle x is in III and
cosx = -4/5, sinx = -3/5
we know cos 2A = 2cos^2 A -1
then
cos x = 2cos^2 (x/2) - 1
-4/5 = 2cos^2 (x/2) - 1
1/5 = 2cos^2 (/2)
cos(x/2) = -1/√10
then using Pythagoras and CAST
sin(x/2) = -3/√10
and
tan (x/2) = (-3/√10) / (-1/√10) = 3
cosx = -4/5, sinx = -3/5
we know cos 2A = 2cos^2 A -1
then
cos x = 2cos^2 (x/2) - 1
-4/5 = 2cos^2 (x/2) - 1
1/5 = 2cos^2 (/2)
cos(x/2) = -1/√10
then using Pythagoras and CAST
sin(x/2) = -3/√10
and
tan (x/2) = (-3/√10) / (-1/√10) = 3