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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Name

Name	one billion four hundred ninety-nine million nine hundred seventy-eight thousand seven hundred ninety-one

Interesting facts

1499978791 has 4 divisors, whose sum is 1500061752
The reverse of 1499978791 is 1978799941
Previous prime number is 26627

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 64
Digital Root 1

Name

Name	one billion one hundred thirty-six million eight hundred ninety-one thousand five hundred fifty-eight

Interesting facts

1136891558 has 32 divisors, whose sum is 2148882048
The reverse of 1136891558 is 8551986311
Previous prime number is 11

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 47
Digital Root 2

Name

Name	one billion two hundred thirty million seven hundred twenty-four thousand twenty-eight

Interesting facts

1230724028 has 8 divisors, whose sum is 2769129072
The reverse of 1230724028 is 8204270321
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 29
Digital Root 2

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