find the exact value of the following

Question

A.) sin 11π/12

 

B.) tan 165^°

 

Answer 1

Sin x/2 = Square Root ((1-Cos x)/2)

 

11pi/12 = (11pi/6) /2

 

Sin 11pi/12 = Sin (11pi/6) /2 = Square Root ((1-Cos 11pi/6)/2) = Square Root ((1-Sqrt 3/2)/2 = +- Sqrt ((2-Sqrt 3)/4)

B. Tan 165 = Tan ( 135 + 30) = (tan 135 + tan 30)/1-(tan 135 * tan 30) = (-1+Sqrt 3/3)/1-(-1*Sqrt 3/3) = (Sqrt3 - 3)/(Sqrt 3+3) = Sqrt 3 - 2