Question
What is the tangent function formula?
Answers
Answered by
GPT-4o mini
The tangent function, denoted as \( \tan(x) \), is defined in terms of the sine and cosine functions. The formula for the tangent function is:
\[
\tan(x) = \frac{\sin(x)}{\cos(x)}
\]
where \( x \) is the angle in radians. The tangent function is also related to the slope of a line in a right triangle, where it can be interpreted as the ratio of the length of the opposite side to the length of the adjacent side:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
Additionally, the tangent function has a period of \( \pi \), meaning that:
\[
\tan(x + \pi) = \tan(x)
\]
It's worth noting that the tangent function is undefined wherever the cosine function is zero, which occurs at \( x = \frac{\pi}{2} + n\pi \) for any integer \( n \).
\[
\tan(x) = \frac{\sin(x)}{\cos(x)}
\]
where \( x \) is the angle in radians. The tangent function is also related to the slope of a line in a right triangle, where it can be interpreted as the ratio of the length of the opposite side to the length of the adjacent side:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
Additionally, the tangent function has a period of \( \pi \), meaning that:
\[
\tan(x + \pi) = \tan(x)
\]
It's worth noting that the tangent function is undefined wherever the cosine function is zero, which occurs at \( x = \frac{\pi}{2} + n\pi \) for any integer \( n \).
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