What Is the Value of tan 90° and Why Is It Undefined?
Discover why tan 90° is undefined and understand the mathematics behind the tangent function's behavior at 90 degrees.
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tan 90° is undefined. This is because the tangent function represents the ratio of the opposite side to the adjacent side in a right-angled triangle, and at 90°, this ratio approaches infinity.
FAQs & Answers
- Why is tan 90° undefined? tan 90° is undefined because the tangent function represents the ratio of the opposite side to the adjacent side in a right-angled triangle, and at 90°, the adjacent side length approaches zero, making the ratio approach infinity.
- What does it mean when a trigonometric function is undefined? A trigonometric function is undefined at points where its value would require division by zero or where it does not have a meaningful finite value.
- How does the tangent function behave near 90°? As the angle approaches 90°, the value of the tangent function increases without bound toward positive or negative infinity, depending on the direction of approach.