Trigonometry Examples

$\sin (π - \frac{π}{6})$

Step 1

To write $π$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\sin (π \cdot \frac{6}{6} - \frac{π}{6})$

Step 2

Combine fractions.

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Step 2.1

Combine $π$ and $\frac{6}{6}$ .

$\sin (\frac{π \cdot 6}{6} - \frac{π}{6})$

Step 2.2

Combine the numerators over the common denominator.

$\sin (\frac{π \cdot 6 - π}{6})$

Step 3

Simplify the numerator.

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Step 3.1

Move $6$ to the left of $π$ .

$\sin (\frac{6 \cdot π - π}{6})$

Step 3.2

Subtract $π$ from $6 π$ .

$\sin (\frac{5 π}{6})$

Step 4

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

$\sin (\frac{π}{6})$

Step 5

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$\frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$