Question

Using a calculator, find which of the following is NOT equal to LaTeX: cot 495°?

Answer 1

To determine which value is NOT equal to \(\cot 495^\circ\), we first need to calculate \(\cot 495^\circ\).

The cotangent function is defined as:
\[
\cot \theta = \frac{1}{\tan \theta}
\]

To find \(\cot 495^\circ\), we can reduce \(495^\circ\) to an equivalent angle within the range \(0^\circ\) to \(360^\circ\):
\[
495^\circ - 360^\circ = 135^\circ
\]

So, \(\cot 495^\circ = \cot 135^\circ\).

Next, we can find \(\cot 135^\circ\):
\[
\cot 135^\circ = \frac{1}{\tan 135^\circ}
\]

Since \(\tan 135^\circ = -1\) (because \(135^\circ\) is in the second quadrant), we have:
\[
\cot 135^\circ = \frac{1}{-1} = -1
\]

Thus,
\[
\cot 495^\circ = -1
\]

Now, any option that is NOT equal to \(-1\) would be the answer. You can test the following values (noted as potential options) with your calculator:

1. \(-1\)
2. \(1\)
3. \(0\)
4. \(-0.5\)

Clearly, any option that is not equal to \(-1\) will answer the question.

Final answer: Any value that is NOT \(-1\) is the correct answer. For example, \(1\) or \(0\) or \(-0.5\) would be options NOT equal to \(\cot 495^\circ\).