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Question Video: Determining Whether a Value Is in the Range of a Trigonometric Function Mathematics • 10th Grade

Is the following statement possible or impossible? cot 𝜃 = −2.

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Video Transcript

Is the following statement possible or impossible? Cot of 𝜃 equals negative two.

This question is really asking, “Is negative two in the range of cotangent?” Here is a graph of cot of 𝜃, and here is the line 𝑦 equals negative two. Does cotangent exist at that point?

It does. In fact, what we’re seeing on this graph is that the range of cotangent is all real numbers. Cotangent can fall on the 𝑦-axis at all real numbers. We know that it’s possible for cotangent to be equal to negative two because the range of cotangent function is all real numbers.

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