Find the exact value of the expression.

Question

sin((pi)/(6))cos((pi)/(3)) - sin((pi)/(3))cos((PI)/(6))

Answer 1

We can write this as a single trig expression.  Since we have a difference in angles for sine,

 

sin(π/6 - π/3) =

sin(π/6 - 2π/6) =

sin(-π/6)

 

-π/6 is the angle π/6 rotated clockwise.  This angle is then in the 4th quadrant.  Since is negative in the 4th quadrant. Therefore,

 

sin(-π/6) = -1/2

Answer 2

Use the Unit Circle:

 

Sin (Pi/6) = Cos (Pi/3) = 1/2

 

Sin (Pi/3) = Cos (Pi/6) = √3/2

 

(1/2)(1/2) - (√3/2)(√3/2) = 1/4 - 3/4 = -1/2