Find the Exact Value cos((7pi)/4-(11pi)/6)

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Trigonometry

$\cos (\frac{7 π}{4} - \frac{11 π}{6})$

To write $\frac{7 π}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\cos (\frac{7 π}{4} \cdot \frac{3}{3} - \frac{11 π}{6})$

To write $\frac{11 π}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\cos (\frac{7 π}{4} \cdot \frac{3}{3} - \frac{11 π}{6} \cdot \frac{2}{2})$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Combine.

$\cos (\frac{7 π \cdot 3}{4 \cdot 3} - \frac{11 π}{6} \cdot \frac{2}{2})$

Multiply $4$ by $3$ .

$\cos (\frac{7 π \cdot 3}{12} - \frac{11 π}{6} \cdot \frac{2}{2})$

Combine.

$\cos (\frac{7 π \cdot 3}{12} - \frac{11 π \cdot 2}{6 \cdot 2})$

Multiply $6$ by $2$ .

$\cos (\frac{7 π \cdot 3}{12} - \frac{11 π \cdot 2}{12})$

Combine the numerators over the common denominator.

$\cos (\frac{7 π \cdot 3 - 11 π \cdot 2}{12})$

Simplify the numerator.

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Multiply $3$ by $7$ .

$\cos (\frac{21 π - 11 π \cdot 2}{12})$

Multiply $2$ by $- 11$ .

$\cos (\frac{21 π - 22 π}{12})$

Subtract $22 π$ from $21 π$ .

$\cos (\frac{- π}{12})$

Move the negative in front of the fraction.

$\cos (- \frac{π}{12})$

Add full rotations of $2 π$ until the angle is between $0$ and $2 π$ .

$\cos (\frac{23 π}{12})$

Evaluate $\cos (\frac{23 π}{12})$ .

$0.96592582$

The result can be shown in multiple forms.

Exact Form:

$\cos (\frac{7 π}{4} - \frac{11 π}{6})$

Decimal Form:

$0.96592582 \dots$

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