Precalculus Examples

$\sin (30) + \sin (150) + \sin (210) + \sin (330)$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$\frac{1}{2} + \sin (150) + \sin (210) + \sin (330)$

Step 1.2

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

$\frac{1}{2} + \sin (30) + \sin (210) + \sin (330)$

Step 1.3

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$\frac{1}{2} + \frac{1}{2} + \sin (210) + \sin (330)$

Step 1.4

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

$\frac{1}{2} + \frac{1}{2} - \sin (30) + \sin (330)$

Step 1.5

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$\frac{1}{2} + \frac{1}{2} - \frac{1}{2} + \sin (330)$

Step 1.6

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.

$\frac{1}{2} + \frac{1}{2} - \frac{1}{2} - \sin (30)$

Step 1.7

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$\frac{1}{2} + \frac{1}{2} - \frac{1}{2} - \frac{1}{2}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{1 + 1 - 1 - 1}{2}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Add $1$ and $1$ .

$\frac{2 - 1 - 1}{2}$

Step 2.2.2

Subtract $1$ from $2$ .

$\frac{1 - 1}{2}$

Step 2.2.3

Subtract $1$ from $1$ .

$\frac{0}{2}$

Step 2.2.4

Divide $0$ by $2$ .

$0$