Question

if \[\sin \frac{ x }{ 2 }=\frac{ 2 }{ 3 }, \left[ 0,\frac{ \pi }{ 2 } \right]\]
Evaluate.
sin(x/4)

Answer 1

hey

Answer 2

just so you know 1/2*x/2=x/4

Answer 3

makes me think we need half angle identity \[\sin^2(\frac{1}{2} \cdot u)=\frac{1}{2}(1-\cos(u)) \\ \text{ where our } u=\frac{x}{2}\]

Answer 4

you are given sin(x/2)=2/3
where x is between 0 and pi/2
draw a right triangle in the first quadrant and find cos(x/2) because you will need this value

Answer 5

I don't quite understand why we use cosine for this question..

Answer 6

do you see the half angle identity above?