Oracle ACOS Function: A Simple Guide

The ACOS function in Oracle SQL is a trigonometric function that stands for Arc Cosine. It does the opposite of the COS (Cosine) function. While COS takes an angle and gives you a ratio, ACOS takes a ratio and gives you back the angle.

The angle is returned in radians, which is the standard mathematical way to measure angles (as opposed to degrees).

What is the ACOS Function in Oracle?

The ACOS function is used to find the angle whose cosine is a given number.

• Input Range: The input number n must be between -1 and 1. This is because the cosine of any angle always falls within this range.
• Output Range: The function returns the angle as a number in radians, which will always be between 0 and pi (approximately 3.14159).

This function is typically used in engineering, scientific, and mathematical calculations where you need to solve for an angle based on a known cosine ratio.

ACOS Function Syntax

The syntax for ACOS is very simple:

ACOS(n)

Let's break that down:

• n: The number (or numeric column) for which you want to find the arc cosine. This value must be between -1 and 1.

Oracle ACOS Function Examples

Here are two practical examples of how to use ACOS.

Example 1: Finding the Arc Cosine of 0.5

In trigonometry, the cosine of a 60-degree angle is 0.5. In radians, 60 degrees is pi / 3 (approx 1.047). Let's see what ACOS returns.

Query:

SELECT 
  ACOS(0.5) AS "ArcCosine_of_0.5"
FROM DUAL;

Result:

ArcCosine_of_0.5
----------------
      1.04719755

This is the angle (in radians) whose cosine is 0.5.

Example 2: Finding the Arc Cosine of -1

The cosine of a 180-degree angle (or pi radians) is -1.

Query:

SELECT 
  ACOS(-1) AS "ArcCosine_of_Neg_1"
FROM DUAL;

Result:

ArcCosine_of_Neg_1
------------------
        3.14159265

This is the value of pi (in radians), which is the angle whose cosine is -1.