Calculus Examples

$\frac{- \frac{1}{1^{2}}}{- 81 π^{2} \cos (9 π)}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$- \frac{1}{1^{2}} \cdot \frac{1}{- 81 π^{2} \cos (9 π)}$

Step 2

One to any power is one.

$- \frac{1}{1} \cdot \frac{1}{- 81 π^{2} \cos (9 π)}$

Step 3

Cancel the common factor of $1$ .

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Step 3.1

Cancel the common factor.

$- \frac{1}{1} \cdot \frac{1}{- 81 π^{2} \cos (9 π)}$

Step 3.2

Rewrite the expression.

$- 1 \cdot 1 \frac{1}{- 81 π^{2} \cos (9 π)}$

Step 4

Multiply $- 1$ by $1$ .

$- \frac{1}{- 81 π^{2} \cos (9 π)}$

Step 5

Separate fractions.

$- (\frac{1}{- 81 π^{2}} \cdot \frac{1}{\cos (9 π)})$

Step 6

Convert from $\frac{1}{\cos (9 π)}$ to $\sec (9 π)$ .

$- (\frac{1}{- 81 π^{2}} \sec (9 π))$

Step 7

Move the negative in front of the fraction.

$- (- \frac{1}{81 π^{2}} \sec (9 π))$

Step 8

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$- (- \frac{1}{81 π^{2}} \sec (π))$

Step 9

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because secant is negative in the second quadrant.

$- (- \frac{1}{81 π^{2}} (- \sec (0)))$

Step 10

The exact value of $\sec (0)$ is $1$ .

$- (- \frac{1}{81 π^{2}} (- 1 \cdot 1))$

Step 11

Multiply $- 1$ by $1$ .

$- (- \frac{1}{81 π^{2}} \cdot - 1)$

Step 12

Multiply $- \frac{1}{81 π^{2}} \cdot - 1$ .

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Step 12.1

Multiply $- 1$ by $- 1$ .

$- (1 \frac{1}{81 π^{2}})$

Step 12.2

Multiply $\frac{1}{81 π^{2}}$ by $1$ .

$- \frac{1}{81 π^{2}}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{81 π^{2}}$

Decimal Form:

$- 0.00125087 \dots$