Trigonometry Examples

$\cos (\frac{7 π}{12} - \frac{5 π}{12})$

Step 1

Combine the numerators over the common denominator.

$\cos (\frac{7 π - 5 π}{12})$

Step 2

Subtract $5 π$ from $7 π$ .

$\cos (\frac{2 π}{12})$

Step 3

Cancel the common factor of $2$ and $12$ .

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Step 3.1

Factor $2$ out of $2 π$ .

$\cos (\frac{2 (π)}{12})$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $12$ .

$\cos (\frac{2 π}{2 \cdot 6})$

Step 3.2.2

Cancel the common factor.

$\cos (\frac{2 π}{2 \cdot 6})$

Step 3.2.3

Rewrite the expression.

$\cos (\frac{π}{6})$

Step 4

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.86602540 \dots$