Find the Exact Value sec(45)

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Trigonometry

$\sec (45)$

The exact value of $\sec (45)$ is $\frac{2}{\sqrt{2}}$ .

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

Multiply $\frac{2}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{2}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Combine and simplify the denominator.

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Multiply $\frac{2}{\sqrt{2}}$ and $\frac{\sqrt{2}}{\sqrt{2}}$ .

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

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{2 \sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{2 \sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 \sqrt{2}}{{\sqrt{2}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{2 \sqrt{2}}{{\sqrt{2}}^{2}}$

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

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Rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\frac{2 \sqrt{2}}{{(2^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2 \sqrt{2}}{2^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{2 \sqrt{2}}{2^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 \sqrt{2}}{2^{\frac{2}{2}}}$

Divide $1$ by $1$ .

$\frac{2 \sqrt{2}}{2^{1}}$

Evaluate the exponent.

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $\sqrt{2}$ by $1$ .

$\sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$

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Name

Name	one hundred sixty-two million eight hundred sixteen thousand four hundred seventy

Interesting facts

162816470 has 8 divisors, whose sum is 293069664
The reverse of 162816470 is 074618261
Previous prime number is 5

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 35
Digital Root 8

Name

Name	three hundred nineteen million eight hundred thousand seven hundred sixty-nine

Interesting facts

319800769 has 4 divisors, whose sum is 323848960
The reverse of 319800769 is 967008913
Previous prime number is 79

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 43
Digital Root 7

Name

Name	one billion two hundred seven million six hundred fifty-two thousand six hundred fifty

Interesting facts

1207652650 has 16 divisors, whose sum is 2608529832
The reverse of 1207652650 is 0562567021
Previous prime number is 5

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 34
Digital Root 7

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