arc tangent

Thân thiện

A student calculates the arc tangent of a ratio on a scientific calculator.

Definition

1. Noun:
   • The inverse function of the tangent: The arc tangent is a mathematical function that, for a given number (the tangent value), returns the corresponding angle. It is the inverse operation of taking the tangent of an angle.

Usage

• The function is used to find an angle when the value of its tangent is known.
• It is commonly abbreviated as or .
• The output (angle) of the function is typically measured in radians or degrees.

Examples

• Noun:
  • To find the angle whose tangent is 1, you calculate the arc tangent of 1, which is 45 degrees or π/4 radians.
  • The value is obtained by applying the arc tangent function to the ratio of the two sides.

Advanced Usage

• Principal Value: The function usually returns the principal value, which is the angle in the range -90° to 90° (-π/2 to π/2 radians).
• Two-Argument Form (atan2): In many programming and engineering contexts, a related two-argument function is used. This function computes the of , but uses the signs of both arguments to determine the correct quadrant of the resulting angle, providing a full 360° range.

Variants and Related Words

• Arctan (n): A common abbreviation for .
  • The result of arctan(0) is 0.
• Atan (n): Another common abbreviation, especially in computing.
  • Use the atan function in your code.
• Inverse Tangent (n): A synonym for .
  • The inverse tangent is a crucial function in trigonometry.

Synonyms

• Inverse Tangent: The function that undoes the tangent operation.
• Arctangent: A single-word variant.

Related Mathematical Functions

• Arc Sine (n): The inverse function of the sine.
• Arc Cosine (n): The inverse function of the cosine.

Học thuật

Noun

1. the inverse function of the tangent; the angle that has a tangent equal to a given number

Từ đồng nghĩa

• arctangent
• arctan
• inverse tangent