Question

Given sinx=1/3 and x is in quadrant 2,find sin x/2and cos x/2

Answer 1

you can sinx as

\[sinx = 2\sin(\frac{x}{2})\cos(\frac{x}{2})\]

Answer 2

no. it is not useful here. let's draw 2nd quadrant

Answer 3

so
sinx = sin(pi - x)

Answer 4

sinx = 1/3
x = arcsin(1/3)

Answer 5

the answer is root 12 - root 6 / 6. How do i get there?

Answer 6

give me one minute

Answer 7

ok

Answer 8

sinx = 1/3 given
\[\cos x = \frac{ =2\sqrt{2} }{ 3 }\]

Answer 9

\[\sin \frac{ x }{ 2 }=\pm \sqrt{\frac{ 1-\cos x }{ 2 }}\]

Answer 10

substitute cosx value in above u get sin x/2

Answer 11

@dayakar excellent. can you prove given answers?

Answer 12

@lochana
am i right

Answer 13

yes. you solved it almost completely. but now we need to find sinx/2 and cox/2

Answer 14

let him try ,if he stuck any where we are here to help

Answer 15

\[\cos \frac{ x }{ 2 }=\pm \sqrt{\frac{ 1+\cos x }{ 2 }}\]

Answer 16

mm.. so get root((3 + root(8))/6) for cosx/2

Answer 17

that not what he is looking for:(

Answer 18

ah it is sonx/2 not cosx/2

Answer 19

no,plz observe ,there is only sign difference

Answer 20

and


it says x exits in 2nd quadrant , that is to say that pi > x > pi/2