Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula.
Sqrt(1-cos50/2)
Recall your half-angle formulas:
sin(x) = sqrt((1-cos(2x))/2)
can you figure out what x is?
To simplify the given expression, we will use the Half-Angle Formula.
The Half-Angle Formula for cosine is given by:
cos(x/2) = ± sqrt((1 + cos(x)) / 2)
In this case, we have the expression sqrt(1 - cos(50/2)).
First, let's calculate cos(50/2):
cos(50/2) = cos(25)
To find the value of cos(25), we can use a calculator or a trigonometric table. We find that cos(25) is approximately 0.9063.
Now, we can substitute the value of cos(50/2) back into the expression:
sqrt(1 - cos(50/2)) = sqrt(1 - 0.9063)
Simplifying further:
sqrt(1 - 0.9063) ≈ sqrt(0.0937) ≈ 0.3061
Therefore, the simplified expression is approximately 0.3061.