SIN

The SIN function in Oracle SQL is used to compute the sine of a given angle, which is a standard trigonometric operation. The SIN function returns the sine value of a number, where the number is an angle in radians.

 

1. Syntax of the SIN Function

The basic syntax for using the SIN function is:

SELECT SIN(angle_in_radians) FROM dual;

• angle_in_radians: The angle in radians for which the sine value is to be calculated.

 

2. What is the SIN Function?

The SIN function returns the sine of an angle provided in radians. In trigonometry, the sine function is a mathematical function that relates the angle of a right triangle to the ratio of the opposite side to the hypotenuse.

• Sine Formula: $$$$sin⁡(θ)=oppositehypotenuse\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} Where θ (theta) is the angle in radians, and the sine of the angle is the ratio of the opposite side to the hypotenuse in a right triangle.

   

  3. Radians vs Degrees

  ·        The input to the SIN function must be in radians. If you have the angle in degrees, you can convert it to radians using the RADIANS function.

  ·        SELECT SIN(RADIANS(30)) FROM dual;  -- Returns the sine of 30 degrees

  ·        The formula to convert from degrees to radians is:

  $$\text{radians} = \frac{\pi \times \text{degrees}}{180}$$

   

  4. Example Queries Using the SIN Function

  a. Sine of a Known Angle (in radians)

  SELECT SIN(PI()/2) AS sine_value FROM dual;

  This returns 1, as the sine of $\frac{\pi}{2}$ (or 90 degrees) is 1.

  b. Using SIN with a Custom Angle in Radians

  SELECT SIN(0.785398) AS sine_value FROM dual;

  This calculates the sine of 0.785398 radians (which is approximately 45 degrees). The result would be around 0.7071.

  c. Sine of an Angle in Degrees (using RADIANS)

  SELECT SIN(RADIANS(60)) AS sine_value FROM dual;

  This computes the sine of 60 degrees. Since $\sin ({60}^{<span\; class="katex">\circ )=32\approx 0.866\backslash sin(60^\backslash circ)\; =\; \backslash frac\{\backslash sqrt\{3\}\}\{2\}\; \backslash approx\; 0.866</span>,\; the\; result\; would\; be\; approximately\; <code><span\; style="line-height:\; 200\%;">0.866</span></code>.}$

   

  5. Range of SIN Values

  The sine of an angle will always be in the range of -1 to 1, regardless of the input angle:

  $$-1\le \sin <span\; class="katex">(\theta )\le 1-1\; \backslash leq\; \backslash sin(\backslash theta)\; \backslash leq\; 1</span>$$

  • SIN(0) will return 0
  • SIN(π) will return 0
  • SIN(π/2) will return 1
  • SIN(3π/2) will return -1

   

  6. Key Points to Remember

  ·        Input: The SIN function in Oracle accepts the angle in radians. If the angle is in degrees, it needs to be converted to radians using the RADIANS function.

  ·        Output: The result will always be a value between -1 and 1, as this is the range of the sine function.

  ·        Mathematical Identity: The sine function is periodic with a period of $2\pi$. That means the sine of any angle can be determined by reducing the angle to a value between $0$ and $2\pi$.

  For example, $\sin(7\pi) = \sin(\pi)$.

   

  7. Performance Considerations

  • Numerical Precision: The result of the SIN function is a floating-point number, and precision may be limited based on the system's numerical handling of floating-point operations.
  • Optimization: The SIN function is a basic mathematical operation, and its performance is generally very efficient. However, if you are performing many trigonometric calculations in a large dataset, ensure that your queries are well-optimized.

   

  8. Practical Use Cases of the SIN Function

  • Wave Analysis: The SIN function can be used to model periodic phenomena such as sound waves, light waves, or tides in a variety of scientific and engineering applications.
  • Geometry and Trigonometry: It is essential in geometric calculations, especially in dealing with right triangles and angles in trigonometric identities.
  • Animations and Graphics: In graphics programming, sine functions are used to create smooth, cyclic animations such as bouncing balls, oscillating objects, and more.