When does tan equal 1?
Understand the Problem
The question is asking for the specific angles or conditions under which the tangent function equals 1. The tangent of an angle in trigonometry is known to be the ratio of the opposite side to the adjacent side of a right triangle, and it equals 1 at certain key angles.
Answer
π/4 + nπ
The angles at which tan(x) equals 1 are x = π/4 + nπ, where n is any integer.
Answer for screen readers
The angles at which tan(x) equals 1 are x = π/4 + nπ, where n is any integer.
More Information
The tangent function reaches 1 at 45° plus every multiple of its period, which is π (180°). This results in a periodic pattern.
Tips
A common mistake is to forget that the tangent function is periodic, thus missing other possible solutions at nπ intervals.
Sources
- Inverse Tan (Inverse Tangent) - Formula, Graph - Cuemath - cuemath.com
- When tanx=1, what does x equal? - Socratic - socratic.org
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