When Is the Tangent Function Positive?

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The tangent function, by definition, is sine over cosine. Find out when the tangent function is positive with help from a mathematics educator with over a decade of experience in this free video clip.

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Video Transcript

Hi, I'm Jimmy Chang, and we're here to talk about and answer the question when is the tangent function positive. Now the tangent function by definition is sine over cosine. Now one obvious location where the tangent function is positive is in quadrant number 1 because in quadrant number 1 both a sine and cosine are positive. So positive over positive is going to be positive. Now, the other way that you can have a positive tangent function or any fraction is positive is when you have negative over negative because negative over negative is positive. Well which quadrant has both the sine negative and when is the cosine negative at the same time? That's actually in quadrant number 3 because in quadrant number 3, both the sine and cosine are negative and therefore that's going to give you a positive tangent value. So the bottom line is, when an angle ends up in quadrant 1 or when an angle ends up in quadrant 3, that is when the tangent function will be positive. So, I'm Jimmy Chang, and that answers the question when is a tangent function positive.

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