If sina =-5÷13 and a lies in quadrant 3 then the value of cos (a÷2)?

1 Answer
Nghi N
May 4, 2018

#cos (a/2) = - sqrt26/26#

Explanation:

#sin a = - 5/13#.
First find cos a.
#cos^2 a = 1 - sin^2 a = 1 - 25/169 = 144/169#
#cos a = +- 12/13#.
Since a lies in Quadrant 3, cos a is negative.
#cos a = - 12/13#.
To find cos (a/2), use trig identity:
#2cos^2 (a/2) = 1 + cos a #
#2cos^2 (a/2) = 1 - 12/13 = 1/13#
#cos^2 (a/2) = 1/26#
#cos (a/2) = +- 1/sqrt26#.
Since a lies in Quadrant 3, then, #a/2# lies in Quadrant 2, and
#cos (a/2)# is negative.
#cos (a/2) = - 1/sqrt26 = sqrt26/26#

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