Trigonometry Examples

$6 \cos (\frac{5 π}{6})$

Step 1

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 second quadrant.

$6 (- \cos (\frac{π}{6}))$

Step 2

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

$6 (- \frac{\sqrt{3}}{2})$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Move the leading negative in $- \frac{\sqrt{3}}{2}$ into the numerator.

$6 \frac{- \sqrt{3}}{2}$

Step 3.2

Factor $2$ out of $6$ .

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

Step 3.3

Cancel the common factor.

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

Step 3.4

Rewrite the expression.

$3 (- \sqrt{3})$

Step 4

Multiply $- 1$ by $3$ .

$- 3 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- 3 \sqrt{3}$

Decimal Form:

$- 5.19615242 \dots$