Question

Using half-angle identities, determine:
1. cos(x/2) if tanx = 12/5 and pi < x < 3pi/2

2. in which quadrant

Answer 1

tanx = 12/5
p^2 + b^2 = h^2
h= 13

cosx = 5/13

x = (inverse) cos5/13...

Answer 2

it is 67.38 the x

Answer 3

but in third quad cos is negative

Answer 4

so cosx = -5/13

Answer 5

and third quadrant

Answer 6

thanks for the answer but im looking for the exact value of cos(x/2).
I think that using half-angle identities is necessary

Answer 7

i forgot it is cosx/2 sorry let me do this again

Answer 8

cosx = -5/13

cos 2* x/2 = 2cos^2 x/2 -1

cosx +1 = 2cos^2 x/2

1 - 5/13 = 2 cos^2 x/2

sqrt(8/(13 *2)) = cosx/2

hers is your answer

and pi<x<3pi/2\

hence pi/2<x < 3pi/4

Answer 9

which is second quadrant

Answer 10

whats the basis for finding the quadrant?

Answer 11

if it is in quadrant 2, then why is tanx = 12/5 and not negative?