Question

What is the exact value of sin (165 degrees)

Answer 1

Answer:

A

Step-by-step explanation:

Think of a value on the unit circle that is double of 165.

330 is that so we can use the double Angle Identity

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

Alpha is 330

so

$\sin(165) = \sqrt{ \frac{1 - \cos(330) }{2} }$

$\sin(165) = \sqrt{ \frac{1 - \frac{ \sqrt{3} }{2} }{2} }$

$\sin(165) = \sqrt{ \frac{ \frac{2 - \sqrt{3} }{2} }{2} }$

$\sin(165) = \sqrt{ \frac{2 - \sqrt{3} }{4} }$

$\sin(165) = \frac{ \sqrt{2 - \sqrt{3} } }{2}$