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

1 Answer
May 4, 2018

cos(a2)=2626

Explanation:

sina=513.
First find cos a.
cos2a=1sin2a=125169=144169
cosa=±1213.
Since a lies in Quadrant 3, cos a is negative.
cosa=1213.
To find cos (a/2), use trig identity:
2cos2(a2)=1+cosa
2cos2(a2)=11213=113
cos2(a2)=126
cos(a2)=±126.
Since a lies in Quadrant 3, then, a2 lies in Quadrant 2, and
cos(a2) is negative.
cos(a2)=126=2626