Here's a breakdown:
* Right Triangle: A triangle with one angle measuring 90 degrees.
* Hypotenuse: The side opposite the right angle, always the longest side.
* Opposite Side: The side directly across from the angle you're considering.
Formula:
sin(angle) = (length of opposite side) / (length of hypotenuse)
Visual Representation:
Imagine a right triangle with an angle 'θ'.
* The sine of that angle is the length of the side opposite 'θ' divided by the length of the hypotenuse.
Key Points:
* The sine of an angle is always a number between -1 and 1 (inclusive).
* The sine function is periodic, meaning it repeats itself over a certain interval.
* The sine function is used extensively in mathematics, physics, engineering, and other fields.
Example:
Consider a right triangle with a 30-degree angle. The sine of 30 degrees is 0.5. This means that the side opposite the 30-degree angle is half the length of the hypotenuse.
Beyond Right Triangles:
While the definition of sine is rooted in right triangles, it can be generalized to any angle using the unit circle. This allows the sine function to be applied to a wider range of applications.