Understanding the Sine Function: Exploring Ratios in Right Triangles and Trigonometry

Sin(x)

The symbol “sin(x)” refers to the sine function

The symbol “sin(x)” refers to the sine function. The sine function is a mathematical function that takes an angle (represented by “x”) as input and returns the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.

In a right triangle, the hypotenuse is the longest side and is opposite the right angle. The side opposite the angle “x” is the side that is not the hypotenuse and is furthest away from the angle “x”.

The sine function is commonly used in trigonometry and is defined as:

sin(x) = opposite / hypotenuse

This means that the sine of an angle “x” is equal to the length of the side opposite the angle divided by the length of the hypotenuse.

The value of sin(x) can vary depending on the value of the angle “x”. The sine function can take any real number as input, but its output range is between -1 and 1. For example, sin(0) = 0, sin(30°) = 1/2, sin(45°) = √2/2, sin(60°) = √3/2, and sin(90°) = 1.

The sine function is periodic, meaning it repeats its values in a specific pattern as the angle increases or decreases. The period of the sine function is 360 degrees or 2π radians. This means that after going through a full rotation, the sine function will repeat its values.

In summary, sin(x) represents the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle. It is a periodic function with values ranging between -1 and 1. The value of sin(x) depends on the angle “x” measured in degrees or radians.

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