Find the Exact Value sin(-60)cos(40)+cos(-60)sin(40)

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.

The exact value of ${\displaystyle \sin \left(60\right)}$ is ${\displaystyle \frac{\sqrt{3}}{2}}$.

Combine ${\displaystyle \cos \left(40\right)}$ and ${\displaystyle \frac{\sqrt{3}}{2}}$.

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

The exact value of ${\displaystyle \cos \left(60\right)}$ is ${\displaystyle \frac{1}{2}}$.

Combine ${\displaystyle \frac{1}{2}}$ and ${\displaystyle \sin \left(40\right)}$.