Use an Addition or Subtraction Formula to find the exact value of the expression

Question

A.) tan(− 11π/12)

B.) cos(13°) cos(32°) − sin(13°) sin(32°)

Answer 1

Use the angles that are on the unit circle.  Then add or subtract those angles to obtain the angle given.

 

A)

 

-11π/12 = - 3π/12 - 4π/12 - 4π/12

            = -π/4 - 2(π/3)

 

tan(-π/4 - 2π/3)

 

π/4 is the reference angle here.  It is in the 4th quadrant because of the negative sign.  You rotate this angle π/3 clockwise 2 times.  After the rotation, the angle ends up in the 3rd quadrant.  The value of tangent is positive in the 3rd quadrant, and tan(π/4) is 1.

 

tan(-11π/12) = 1

 

 

B)

 

This is a addition angle identity for cosine.

 

cos(13 + 32) = cos(45) = √(2)/2