Question

If sin θ = 1, then the value of `1/2  sin(theta/2)`is ______.

Options

• `1/(2sqrt(2))`

• `1/sqrt(2)`

• `1/2`

• 0

Answer 1

If sin θ = 1, then the value of `1/2  sin(theta/2)`is `bbunderline(1/(2sqrt(2)))`.

Explanation:

`sin(theta/2)=+-sqrt((1-costheta)/2)`

`=+-sqrt((1-0)/2)=+-1/sqrt(2)`

Since we are interested in the positive square root (as the principal value for θ = `pi/2` will result in a positive sine value for `theta/2`, we have

`sin(theta/2)=1/sqrt(2)`

Therefore, the value of `1/2  sin (theta/2)`is 

`=1/2xx1/sqrt(2)=1/(2sqrt(2))`