Question

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

Answer 1

Answer:

sin 15° = 0.2588

Step-by-step explanation:

The half angle formula is:

$\sin{(\frac{x}{2})} = \pm \sqrt{\frac{1 - \cos{x}}{2}}$

sin 15°

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

$\sin{15} = sqrt{\frac{1 - \cos{30}}{2}}$

Since $\cos{30} = 0.866$

$\sin{15} = sqrt{\frac{1 - \cos{30}}{2}} = \sqrt{\frac{1 - 0.866}{2}} = 0.2588$

sin 15° = 0.2588