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

1 Answer
Mar 14, 2018

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