How Do You Find the Value of Arctan 0?

Arctan, like arcsin and arccos, is an inverse trignometric function that determines at what angle a given fraction occurs. Inverse trigonometric functions can be found with a calculator in under a minute or with pen and paper in a few minutes.

1. Know how tan and arctan work

The tangent of an angle in a right triangle is the fraction found by dividing the side opposite the angle by the side adjacent to the angle. For example the tangent of 45 degrees is 1 because the base (adjacent) and height (opposite) of an isosceles right triangle are always equal. Tangent operations are often written as tan(x). The inverse tangent, or arctan, reverses the operation. For example arctan(1) = 45 degrees because tan(45) = 1.

2. Find an angle whose tangent is 0

To have a 0 tangent, an angle must create a triangle where the opposite side length is 0 and the adjacent is a nonzero number. If you think of the opposite side as the height or vertical value and the adjacent as the base or horizontal value, the tangent of an angle is 0 whenever the tangent creates a horizontal ray. A calculator can confirm that the horizontal condition is met at 0 degrees: arctan(0) = 0

3. Rewrite it as a function of k

Tangent is a periodical function. The arctan function produces multiple values for every angle. The tangent is 0 at 0 degrees and at 180 and 360 degrees. The angle is horizontal every 180 degrees. Therefore, in degrees arctan(0) = k180, where k is any integer, including 0.

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