Calculus Examples

$lim_{x \to 5} \frac{\cos (5 π)}{6}$

Step 1

Evaluate the limit of $\frac{\cos (5 π)}{6}$ which is constant as $x$ approaches $5$ .

$\frac{\cos (5 π)}{6}$

Step 2

Simplify the answer.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

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

$\frac{\cos (π)}{6}$

Step 2.1.2

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

$\frac{- \cos (0)}{6}$

Step 2.1.3

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

$\frac{- 1 \cdot 1}{6}$

Step 2.1.4

Multiply $- 1$ by $1$ .

$\frac{- 1}{6}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{1}{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{6}$

Decimal Form:

$- 0.1\overline{6}$