Trigonometry Examples

- \frac{5 π}{6}

$- \frac{5 π}{6}$

Step 1

Take the cosine of

- \frac{5 π}{6}

$- \frac{5 π}{6}$ .

\cos (- \frac{5 π}{6})

$\cos (- \frac{5 π}{6})$

Step 2

Add full rotations of

2 π

$2 π$ until the angle is greater than or equal to

0

$0$ and less than

2 π

$2 π$ .

\cos (\frac{7 π}{6})

$\cos (\frac{7 π}{6})$

Step 3

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

- \cos (\frac{π}{6})

$- \cos (\frac{π}{6})$

Step 4

The exact value of

\cos (\frac{π}{6})

$\cos (\frac{π}{6})$ is

\frac{\sqrt{3}}{2}

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

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

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

Decimal Form:

- 0.86602540 \dots

$- 0.86602540 \dots$