Answer:
To find the value of sin 15, we can use the half-angle formula for sine:
sin (θ/2) = ±√[(1 - cos θ)/2]
where θ is the angle in radians.
In this case, we want to find sin 15, which is half of 30. So we can write:
sin 15 = sin (30/2)
Using the half-angle formula for sine with θ = 30, we have:
sin 15 = ±√[(1 - cos 30)/2]
We are given that cos 30 = √3/2, so we can substitute this value into the formula:
sin 15 = ±√[(1 - √3/2)/2]
To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by √2:
sin 15 = ±√[(√2 - √6)/4]
Since 0° < 15° < 90°, the sine of 15 degrees is positive. So we can take the positive square root:
sin 15 = √[(√2 - √6)/4]
Therefore, the value of sin 15 is:
sin 15 = √[(√2 - √6)/4]