Trigonometry Examples

$\sin (\frac{- 13 π}{6})$

Step 1

Move the negative in front of the fraction.

$\sin (- \frac{13 π}{6})$

Step 2

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\sin (\frac{11 π}{6})$

Step 3

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.

$- \sin (\frac{π}{6})$

Step 4

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

$- \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$