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As tan π4=1, this means that arctan1=π4.

Thus, arctan1 =π4.

It turns out that arctan and cot are really separate things: cot(x) = 1 / tan (x), so cotangent is basically the reciprocal of a tangent, or, in other words, the multiplicative inverse. arctan (x) is the angle whose tangent is x.

Using the unit circle we can see that tan(1)= pi/4. Since the “Odds and Evens Identity” states that tan(-x) = -tan(x). Tan(-1)= -pi/4.

Arctangent table

y | x = arctan (y) | |
---|---|---|

degrees | radians | |

0 | 0 ° | 0 |

0.577350269 | 30° | π /6 |

1 | 45° | π /4 |

If so, use the Sin and Asin functions for conversions.) To convert degrees of slope into percentage of slope, use Slope-in-percent = Tan(Slope-in-degrees * Pi/180). To convert slope in percentage to slope in degrees, use Slope-in-degrees = Atan (slope-in-percent)*180/Pi.

By convention, the range of arctan is limited to -90° to +90° *. So if you use a calculator to solve say arctan 0.55, out of the infinite number of possibilities it would return 28.81°, the one in the range of the function. For y = arctan x:

Range | − π 2 < y < + π 2 − 90 ° < y < + 90 ° |
---|---|

Domain | All real numbers |

The arctangent is the inverse tangent function. The limit of arctangent of x when x is approaching infinity is equal to pi/2 radians or 90 degrees: The limit of arctangent of x when x is approaching minus infinity is equal to -pi/2 radians or -90 degrees: Arctan ►

The value for arctan ( 0 ) is 0º or 0 radians.

Basic idea: To find tan ^{–} ^{1} 1, we ask “what angle has tangent equal to 1?” The answer is 45°.

The tangent function for acute angles can be viewed as the ratio of the opposite to the adjacent side of the angle. If the ratio is 1, it means that the triangle is a right angle isosceles and therefore the corresponding angle is 45 degrees of π4 rad.

The symbol for inverse sine is sin ^{–} ^{1}, or sometimes arcsin.

The tangent of x is defined to be its sine divided by its cosine: tan x = sin x cos x. The secant of x is 1 divided by the cosine of x: sec x = 1 cos x, and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x.

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