Expand Using Sum/Difference Formulas csc(pi/2-theta)

$\csc (\frac{π}{2} - θ)$

Replace $\csc (\frac{π}{2} - θ)$ with an equivalent expression $\frac{1}{\sin (\frac{π}{2} - θ)}$ using the fundamental identities.

$\frac{1}{\sin (\frac{π}{2} - θ)}$

Use a sum or difference formula on the denominator.

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Use the difference formula for sine to simplify the expression. The formula states that $\sin (A - B) = \sin (A) \cos (B) - \cos (A) \sin (B)$ .

$\frac{1}{\sin (\frac{π}{2}) \cos (θ) - \cos (\frac{π}{2}) \sin (θ)}$

Remove parentheses.

$\frac{1}{\sin (\frac{π}{2}) \cos (θ) - \cos (\frac{π}{2}) \sin (θ)}$

Simplify each term.

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The exact value of $\sin (\frac{π}{2})$ is $1$ .

$\frac{1}{1 \cos (θ) - \cos (\frac{π}{2}) \sin (θ)}$

Multiply $\cos (θ)$ by $1$ .

$\frac{1}{\cos (θ) - \cos (\frac{π}{2}) \sin (θ)}$

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$\frac{1}{\cos (θ) + 0 \sin (θ)}$

Multiply $- 1$ by $0$ .

$\frac{1}{\cos (θ) + 0 \sin (θ)}$

Multiply $0$ by $\sin (θ)$ .

$\frac{1}{\cos (θ) + 0}$

Add $\cos (θ)$ and $0$ .

$\frac{1}{\cos (θ)}$

Convert from $\frac{1}{\cos (θ)}$ to $\sec (θ)$ .

$\sec (θ)$

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Name

Name	two billion three million five hundred ninety thousand three hundred eighteen

Interesting facts

2003590318 has 32 divisors, whose sum is 3368563200
The reverse of 2003590318 is 8130953002
Previous prime number is 179

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 31
Digital Root 4

Name

Name	eight hundred forty-nine million one hundred fifty-six thousand six hundred thirty-five

Interesting facts

849156635 has 8 divisors, whose sum is 1019149296
The reverse of 849156635 is 536651948
Previous prime number is 10141

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 47
Digital Root 2

Name

Name	one billion three hundred forty-seven million two hundred sixteen thousand two hundred twenty-two

Interesting facts

1347216222 has 32 divisors, whose sum is 2994848640
The reverse of 1347216222 is 2226127431
Previous prime number is 53

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 30
Digital Root 3

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Evaluate square root of 319

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Solve the Triangle tri{3}{30}{}{}{4}{}