Question

if cos x=2/3 and x is in quadrant 4 then sin x/2=

A. 1/3
B. Sqrt 1/6
C. -Sqrt 1/6
D. -1/3

Options are above will mark brainliest

Answer 1

Answer: B, $\sqrt{\frac{1}{6} }$

Step-by-step explanation:

Using half-angle identities

Using half angle identities, we know that

$sin\frac{x}{2} = +/- \sqrt{\frac{1-cosx}{2} }$

Plug in 2/3 for cosx

$sin\frac{x}{2} = +/- \sqrt{\frac{1-2/3}{2} }$

$sin\frac{x}{2} = +/- \sqrt{\frac{1/3}{2} }$

$sin\frac{x}{2} = +/- \sqrt{\frac{1}{6} }$

Determining sign

Since the angle x is in quadrant 4 from 270 to 360 degrees, if we divide the angle by 2, the angle x should be somewhere from 135 to 180 degrees, which would all fall in quadrant 2

all sin values in quadrant 2 are positive

Final answer

$sinx = \sqrt{\frac{1}{6} }$