Expand the Trigonometric Expression cos(pi/5+pi/6)

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Trigonometry

$\cos (\frac{π}{5} + \frac{π}{6})$

To write $\frac{π}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\cos (\frac{π}{5} \cdot \frac{6}{6} + \frac{π}{6})$

To write $\frac{π}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\cos (\frac{π}{5} \cdot \frac{6}{6} + \frac{π}{6} \cdot \frac{5}{5})$

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{π}{5}$ and $\frac{6}{6}$ .

$\cos (\frac{π \cdot 6}{5 \cdot 6} + \frac{π}{6} \cdot \frac{5}{5})$

Multiply $5$ by $6$ .

$\cos (\frac{π \cdot 6}{30} + \frac{π}{6} \cdot \frac{5}{5})$

Multiply $\frac{π}{6}$ and $\frac{5}{5}$ .

$\cos (\frac{π \cdot 6}{30} + \frac{π \cdot 5}{6 \cdot 5})$

Multiply $6$ by $5$ .

$\cos (\frac{π \cdot 6}{30} + \frac{π \cdot 5}{30})$

Combine the numerators over the common denominator.

$\cos (\frac{π \cdot 6 + π \cdot 5}{30})$

Simplify the numerator.

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Move $6$ to the left of $π$ .

$\cos (\frac{6 \cdot π + π \cdot 5}{30})$

Move $5$ to the left of $π$ .

$\cos (\frac{6 π + 5 \cdot π}{30})$

Add $6 π$ and $5 π$ .

$\cos (\frac{11 π}{30})$

Evaluate $\cos (\frac{11 π}{30})$ .

$0.40673664$

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Name

Name	seven hundred ninety-two million five hundred eighty-four thousand five hundred thirty-two

Interesting facts

792584532 has 32 divisors, whose sum is 1988639640
The reverse of 792584532 is 235485297
Previous prime number is 277

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 45
Digital Root 9

Name

Name	sixty-seven million six hundred sixty thousand five hundred seventy-two

Interesting facts

67660572 has 128 divisors, whose sum is 276701184
The reverse of 67660572 is 27506676
Previous prime number is 23

Basic properties

Is Prime? no
Number parity even
Number length 8
Sum of Digits 39
Digital Root 3

Name

Name	one billion one hundred sixty-six million two hundred thirty thousand three hundred twenty-four

Interesting facts

1166230324 has 16 divisors, whose sum is 2998878048
The reverse of 1166230324 is 4230326611
Previous prime number is 7

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 28
Digital Root 1

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