Question

Use the half-angle formulas to find the exact value of the trigonometric function sin 15°

Answer 1

sin 15° = 0.2588

Explanation:

The half angle formula is:

`\sin{((x)/(2))} = \pm \sqrt{(1 - cos(x))/(2)}`

sin 15°

The double of 15º is 30º. First quadrant, so the sine is positive.

`sin(15) = sqrt{(1 - cos(30))/(2)}`

Since
`cos(30) = 0.866`

`sin(15) = sqrt{(1 - cos(30))/(2)} = \sqrt{(1 - 0.866)/(2)} = 0.2588`

sin 15° = 0.2588