Question

if cosx = 2/3 and x is in quadrant 4, then sin x/2=?

Answer 1

answer choices:
A) 1/3
B) Rad (1/6)
C) -1/3
D)-Rad(1/6)

Answer 2

first you need \(\sin(x)\)

Answer 3

do you know how to find it?
in other words: if you know \(\cos(x)=\frac{2}{3}\) can you find \(\sin(x)\) ?

Answer 4

/\[\sqrt{\sqrt{5}}/3\] right?

Answer 5

forget the 2nd rad on the 5

Answer 6

yes, but now i just realized i steered you wrong, since
\[\sin(\frac{x}{2})=\pm\sqrt{\frac{1-\cos(x)}{2}}\] so really you do not need \(\sin(x)\) for this, i was mistaken (you were right though)

Answer 7

so in x would it be 4/3?

Answer 8

plug in \(\frac{2}{3}\) where you see \(\cos(x)\)

Answer 9

\[\sin(\frac{x}{2})=\pm\sqrt{\frac{1-\cos(x)}{2}}=\pm\sqrt{\frac{1-\frac{2}{3}}{2}}\]

Answer 10

now we have some arithmetic to do , and also have to figure out if it is plus or minus
since \(x\) is in quadrant 4, \(\frac{x}{2}\) is in quadrant 2, therefore \(\sin(\frac{x}{2})\) is positive

Answer 11

you good with the arithmetic?

Answer 12

yea thanks a bunch!

Answer 13

also
one more thing

Answer 14

sure, columbo