Precalculus Examples

$\cot (\frac{38 π}{4})$

Step 1

Cancel the common factor of $38$ and $4$ .

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Step 1.1

Factor $2$ out of $38 π$ .

$\cot (\frac{2 (19 π)}{4})$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $4$ .

$\cot (\frac{2 (19 π)}{2 (2)})$

Step 1.2.2

Cancel the common factor.

$\cot (\frac{2 (19 π)}{2 \cdot 2})$

Step 1.2.3

Rewrite the expression.

$\cot (\frac{19 π}{2})$

Step 2

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

$\cot (\frac{3 π}{2})$

Step 3

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

$- \cot (\frac{π}{2})$

Step 4

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

$- 0$

Step 5

Multiply $- 1$ by $0$ .

$0$