Question

Given `sin theta=4/5`, `theta` lies in Quadrant 2, find `cos theta/2` ?

Answer 1

`costheta/2= -3/10`

Explanation:

It lies in the second quadrant
So here is what I know:
Sin(y-value) is positive
Cos(x-value) is negative

I also know that `sintheta` is Opposite/Hypotenuse
Therefore: `4` is the length of the opposite leg and the length of the hypotenuse is `5`

We can either use Pythagorean theorem to find the length of the adjacent leg or we can apply a Pythagorean triple:
Pythagorean Theorem: `a^2+b^2=c^2`
Manipulated to: `b=+-sqrt(c^2-a^2)`
`b=+-sqrt((5)^2-(4)^2)`
`b=+-sqrt(25-16)`
`b=+-sqrt(9)`
`b=+-3`
Since 4 is supposed to be the Cos value, we will use `-3`

`costheta=-3/5`

Therefore: `costheta/2= (-3/5)/2`

`costheta/2= -3/10`