Arctan, also written as tan-1 or atan, is equal to the angle whose tangent is a given number. In simpler terms, it's the inverse tangent function.
Understanding Arctan
Arctan answers the question: "What angle, when you take its tangent, gives you this number?" It's used to find the angle (typically represented as θ) when you know the ratio of the opposite side (perpendicular) to the adjacent side (base) in a right-angled triangle.
Arctan Formula
The fundamental formula is:
arctan (opposite / adjacent) = θ
Where:
oppositeis the length of the side opposite to the angle θ.adjacentis the length of the side adjacent to the angle θ.θis the angle (usually in radians or degrees).
Example
If you have a right-angled triangle where the opposite side is 3 and the adjacent side is 4, then:
arctan (3/4) = θ
Using a calculator, you'll find that θ ≈ 36.87 degrees or ≈ 0.64 radians. This means the angle whose tangent is 0.75 (3/4) is approximately 36.87 degrees or 0.64 radians.
Range of Arctan
The arctan function has a range of (-π/2, π/2) radians or (-90°, 90°) degrees. This means that the arctan function will always return an angle within this interval.
Arctan in Calculations
Arctan is widely used in various fields like:
- Physics: Calculating angles in projectile motion or wave mechanics.
- Engineering: Determining angles in structural designs or control systems.
- Computer Graphics: Calculating viewing angles or rotations in 3D rendering.
In summary, arctan is the inverse tangent function that gives you the angle corresponding to a given tangent value, specifically used to find angles in right-angled triangles based on the ratio of the opposite and adjacent sides.
