Video: Determining Whether a Value Is in the Range of a Trigonometric Function

Is the following statement possible or impossible? cot ๐œƒ = โˆ’2.

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Video Transcript

Is the following statement possible or impossible? Cot of ๐œƒ equals negative two.

This question is really asking, โ€œIs negative two in the range of cotangent?โ€ Here is a graph of cot of ๐œƒ, and here is the line ๐‘ฆ equals negative two. Does cotangent exist at that point?

It does. In fact, what weโ€™re seeing on this graph is that the range of cotangent is all real numbers. Cotangent can fall on the ๐‘ฆ-axis at all real numbers. We know that itโ€™s possible for cotangent to be equal to negative two because the range of cotangent function is all real numbers.

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