Question

exact value of sin(11pi/12)

Answer 1

Answer:

$\frac{ - \sqrt{2} + \sqrt{6} }{4}$

Step-by-step explanation:

Write 11pi/12 as a sum.

$\sin( \frac{11\pi}{12} ) = \sin( \frac{\pi}{6} + \frac{3\pi}{4} )$

Using sin(t+s)= sin(t)cos(s) + cos(t)sin(s), expand the expression.

$\sin( \frac{\pi}{6} ) \cos( \frac{3\pi}{4} ) + \cos( \frac{\pi}{6} ) \sin( \frac{3\pi}{4} )$

Using trigonometric values, calculate.

$\frac{1}{2} \times ( - \frac{ \sqrt{2} }{2} ) + \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{2} }{2}$

Multiply to get

$- \frac{ \sqrt{2} }{4} \ + \frac{ \sqrt{6} }{4}$

Which equals

$\frac{ - \sqrt{2} + \sqrt{6} }{4}$

Hope this helps!