Precalculus Examples

$- \cot (\frac{π}{4} + 11 π)$

Step 1

To write $11 π$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \cot (\frac{π}{4} + 11 π \cdot \frac{4}{4})$

Step 2

Combine fractions.

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Step 2.1

Combine $11 π$ and $\frac{4}{4}$ .

$- \cot (\frac{π}{4} + \frac{11 π \cdot 4}{4})$

Step 2.2

Combine the numerators over the common denominator.

$- \cot (\frac{π + 11 π \cdot 4}{4})$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $4$ by $11$ .

$- \cot (\frac{π + 44 π}{4})$

Step 3.2

Add $π$ and $44 π$ .

$- \cot (\frac{45 π}{4})$

Step 4

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

$- \cot (\frac{5 π}{4})$

Step 5

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$- \cot (\frac{π}{4})$

Step 6

The exact value of $\cot (\frac{π}{4})$ is $1$ .

$- 1 \cdot 1$

Step 7

Multiply $- 1$ by $1$ .

$- 1$