How do you find the exact values of sin 15 degrees using the half angle formula?
Using the Half Angle Formula:
We choose the positive one.
Find exact value of
Consider the half-angle formula for sine:
Since we know that 15 is half of 30, we can plug
or see slightly more advanced method to remove nested root (at the bottom)
which is our answer, but has a nested root
Removing nested root from answer:
Let us multiply both the numerator and denominator inside the square root by
Now we can write
We can take out a
We can rationalize the denominator:
which is our answer without a nested root.
We also know
Plugging in the values, we get
Simplifying, we get