Find the Exact Value cos(30 degrees )+cos(150 degrees )+cos(210 degrees )+cos(330 degrees )

The exact value of ${\displaystyle \cos \left(30°\right)}$ is ${\displaystyle \frac{\sqrt{3}}{2}}$.

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

The exact value of ${\displaystyle \cos \left(30\right)}$ is ${\displaystyle \frac{\sqrt{3}}{2}}$.

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

The exact value of ${\displaystyle \cos \left(30\right)}$ is ${\displaystyle \frac{\sqrt{3}}{2}}$.

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

The exact value of ${\displaystyle \cos \left(30\right)}$ is ${\displaystyle \frac{\sqrt{3}}{2}}$.

Combine the numerators over the common denominator.

Subtract ${\displaystyle \sqrt{3}}$ from ${\displaystyle \sqrt{3}}$.

Subtract ${\displaystyle \sqrt{3}}$ from ${\displaystyle 0}$.

Add ${\displaystyle -\sqrt{3}}$ and ${\displaystyle \sqrt{3}}$.

Divide ${\displaystyle 0}$ by ${\displaystyle 2}$.