Trigonometry Examples

$\cos (- \frac{5}{6} \cdot π)$

Step 1

Combine $π$ and $\frac{5}{6}$ .

$\cos (- \frac{π \cdot 5}{6})$

Step 2

Move $5$ to the left of $π$ .

$\cos (- \frac{5 \cdot π}{6})$

Step 3

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

$\cos (\frac{7 π}{6})$

Step 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.

$- \cos (\frac{π}{6})$

Step 5

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.86602540 \dots$