Question

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

Answer 1

`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`