Question

Find the exact value of sinpi/12

Answer 1

Answer:0.2588

Step-by-step explanation:

To find the exact value for

Sinpi/12

pi=180°

So

Sin 180/12

Sin15°

=0.2588

Answer 2

Answer:

Step-by-step explanation:

The answer given below is not in the form you need.  You need the form that includes radicals, not decimals.  The formula for the half angle of sin is

$sin(\frac{\theta}{2})=+/-\sqrt{\frac{1-cos\theta}{2} }$ so we need to find out what theta is.  If our problem is

$sin(\frac{\pi}{12})$ , to get that into half angle form, it would be rewritten as

$sin(\frac{\frac{\pi}{6} }{2})$ so

$\theta=\frac{\pi}{6}$

Look to your unit circle to find the EXACT VALUE of the cos of that angle.  

$cos(\frac{\pi}{6})=\frac{\sqrt{3} }{2}$

Filling that into the formula for the half angle sin:

$sin(\frac{\frac{\pi}{6} }{2})=+/-\sqrt{\frac{1-\frac{\sqrt{3} }{2} }{2} }$  Doing a bit of simplifying gives you

$+/-\sqrt{\frac{\frac{2}{2} -\frac{\sqrt{3} }{2} }{2} }$ and

$+/-\sqrt{\frac{\frac{2-\sqrt{3} }{2} }{2} }$  and

$+/-\sqrt{\frac{2-\sqrt{3} }{2}* \frac{1}{2} }$ gives you

$+/-\sqrt{\frac{2-\sqrt{3} }{4} }$ which finally simplifies to

$+/-\frac{\sqrt{2-\sqrt{3} } }{2}$

That's the answer in exact format.