Algebra Examples

$\cos (30 °) + \cos (150 °) + \cos (210 °) + \cos (330 °)$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{\sqrt{3}}{2} + \cos (150 °) + \cos (210 °) + \cos (330 °)$

Step 1.2

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.

$\frac{\sqrt{3}}{2} - \cos (30) + \cos (210 °) + \cos (330 °)$

Step 1.3

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

$\frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2} + \cos (210 °) + \cos (330 °)$

Step 1.4

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.

$\frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2} - \cos (30) + \cos (330 °)$

Step 1.5

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

$\frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2} + \cos (330 °)$

Step 1.6

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

$\frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2} + \cos (30)$

Step 1.7

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

$\frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2} - \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{\sqrt{3} - \sqrt{3} - \sqrt{3} + \sqrt{3}}{2}$

Step 2.2

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

$\frac{0 - \sqrt{3} + \sqrt{3}}{2}$

Step 2.3

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

$\frac{- \sqrt{3} + \sqrt{3}}{2}$

Step 2.4

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

$\frac{0}{2}$

Step 2.5

Divide $0$ by $2$ .

$0$