Find sin x 2 cos x 2 and tan x 2 from the given informatio

Find sin x 2 , cos x 2 , and tan x 2 from the given information. sec x = 10 /9 , 270° < x < 360°

sec x = 10 /9 , 270° < x < 360°

cosx = 9/10

I understand we have to find sinx/2, cosx/2, tanx/2

sinx/2:

use the formula: sin(x/2) = sqrt{(1 -cosx)/2}

sin(x/2) = sqrt{(1 -9/10)/2} = 1/sqrt(20) = 1/2sqrt5

cos(x/2) = sqrt{(1+cosx)/2}

= sqrt{(1 +9/10)/2} = sqrt(19)/2sqrt5

tan(x/2)= sinx/2/cosx/2

= (1/2sqrt5)/(sqrt(19)/2sqrt5)

= 1/sqrt19