Basic Math Examples

$- \csc^{2} (\frac{π}{4}) \frac{π}{4} \cdot 3$

Step 1

The exact value of $\csc (\frac{π}{4})$ is $\sqrt{2}$ .

$- {\sqrt{2}}^{2} \frac{π}{4} \cdot 3$

Step 2

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

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$- {(2^{\frac{1}{2}})}^{2} \frac{π}{4} \cdot 3$

Step 2.2

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

$- 2^{\frac{1}{2} \cdot 2} \frac{π}{4} \cdot 3$

Step 2.3

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

$- 2^{\frac{2}{2}} \frac{π}{4} \cdot 3$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$- 2^{\frac{2}{2}} \frac{π}{4} \cdot 3$

Step 2.4.2

Rewrite the expression.

$- 2^{1} \frac{π}{4} \cdot 3$

Step 2.5

Evaluate the exponent.

$- 1 \cdot 2 \frac{π}{4} \cdot 3$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $- 1 \cdot 2$ .

$2 \cdot - 1 \frac{π}{4} \cdot 3$

Step 3.2

Factor $2$ out of $4$ .

$2 \cdot - 1 \frac{π}{2 (2)} \cdot 3$

Step 3.3

Cancel the common factor.

$2 \cdot - 1 \frac{π}{2 \cdot 2} \cdot 3$

Step 3.4

Rewrite the expression.

$- 1 \frac{π}{2} \cdot 3$

Step 4

Rewrite $- 1 \frac{π}{2}$ as $- \frac{π}{2}$ .

$- \frac{π}{2} \cdot 3$

Step 5

Multiply $- \frac{π}{2} \cdot 3$ .

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Step 5.1

Multiply $3$ by $- 1$ .

$- 3 \frac{π}{2}$

Step 5.2

Combine $- 3$ and $\frac{π}{2}$ .

$\frac{- 3 π}{2}$

Step 6

Move the negative in front of the fraction.

$- \frac{3 π}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{3 π}{2}$

Decimal Form:

$- 4.71238898 \dots$