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Guilherme Mazui

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What is the Difference Between Sine and Arcsine?

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The sine function and arcsine (or inverse sine) function are related but distinct concepts in trigonometry. Here are the main differences between them:

  • Sine: The sine function is a basic trigonometric function that represents the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right-angled triangle. In other words, given an angle, the sine function provides the ratio of the opposite side to the hypotenuse. The range of the sine function is between -1 and +1.
  • Arcsine: The arcsine function, also known as the inverse sine function, is the inverse of the sine function. It takes a value between -1 and +1 and returns the angle whose sine function is equal to that value. In other words, if you know the ratio of the opposite side to the hypotenuse, the arcsine function gives you the angle. The range of the arcsine function is from -π to +π radians.

In summary:

  • The sine function maps an angle to a value between -1 and +1, representing the ratio of the opposite side to the hypotenuse in a right-angled triangle.
  • The arcsine (inverse sine) function takes a value between -1 and +1 and returns the angle whose sine function is equal to that value.
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  • What is the Difference Between Sine and Arcsine?
  • Comparative Table: Sine vs Arcsine

    • Comparative Table: Sine vs Arcsine

    The sine function and arcsine function are related but serve different purposes. Here is a table highlighting the differences between them:

    Feature Sine Function Arcsine Function
    Definition The sine function is a mathematical operation that calculates the ratio of the length of the side opposite the angle to the length of the hypotenuse (the side opposite the right angle) in a right-angled triangle The arcsine (or inverse sine) function is the inverse of the sine function, meaning it takes the ratio of the opposite side to the hypotenuse and calculates the angle
    Notation Sin(θ) Sin-1(θ) or Arcsin(θ)
    Domain -∞ to +∞ -1 to +1
    Range -1 to +1 -π/2 to +π/2
    Function Type Many-to-one One-to-one
    Graph Wave-like shape Restricted to 1st and 4th quadrants

    The sine function takes an angle as input and outputs a value between -1 and 1, representing the ratio of the opposite side to the hypotenuse. The arcsine function, on the other hand, takes the ratio of the opposite side to the hypotenuse as input and outputs the corresponding angle, restricted to the range of [-π/2, π/2] radians or [-90°, 90°] degrees.

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    Guilherme Mazui

    Guilherme Mazui is graduated in journalism from the Federal University of Minas Gerais (UFMG) and a master's degree in Communication from the University of São Paulo (USP). In addition, he has experience in advertising writing and has worked as a content editor in several companies.