Question

Help please?

Answer 1

`sin(phi/2) = (3sqrt(10))/10 approx 0.9`, C

Explanation:

We know the half angle formula:
`sin(phi/2) = pm sqrt((1-cos(phi))/2)`

This means
`sin(phi/2) = pm 3/sqrt(10)`

Based on the angle, we can think of the unit circle. If `180 < phi < 270`, `90 < phi/2 < 135`, so this is in the second quadrant, meaning that `sin(phi/2)` must be positive. Therefore,

`sin(phi/2) = (3sqrt(10))/10`
We can numerically approximate this as
`3/10 sqrt(10) approx 0.3 sqrt(9) = 0.9`

However, we could have immediately gotten this answer without any of this fancy math. Since sine is always between -1 and 1, it's either B or C. By the same logic above, the answer must be positive, so it must be C.