What does Sin, Cos, Tan actually mean? Trigonometry explained for Beginners!

The paragraph introduces the concept of trigonometric functions, specifically sine, cosine, and tangent, as nouns that represent abstract mathematical functions rather than tangible objects. It draws an analogy with the concept of 'price' as a function, explaining that just like 'price', these functions take an input and produce an output. The input for these functions is an angle, and the output is a numerical value. The explanation includes the idea of angles and how they relate to the unit circle, emphasizing that these functions are not physical objects but mathematical concepts.

This paragraph delves into the mathematical notation used for functions, using the example of the 'price' function to illustrate how inputs and outputs are represented. It then applies this notation to sine, cosine, and tangent functions, showing how angles are used as inputs. The paragraph also introduces the concept of an open function, where the input is represented by a variable (like 'x' or 'θ'), which can take any value within a specified range, such as 0 to 360 degrees for angles.

The explanation shifts to the unit circle, a visual tool used to understand sine, cosine, and tangent functions. The unit circle is defined and its relationship to angles and their corresponding coordinates (x and y) is explored. The paragraph describes how moving a point around the unit circle at various angles (45, 90, 135, 180, 270, and 70 degrees) results in different x and y coordinates, which correspond to the cosine and sine of those angles, respectively.

This section continues the exploration of angles on the unit circle, focusing on how the position of an angle (magnet) affects its x and y coordinates. The explanation includes a detailed look at how the horizontal (x) and vertical (y) shifts of the magnet correspond to the cosine and sine values, respectively. The paragraph provides examples of calculating these values at different angles, such as 45, 90, 180, and 270 degrees, and emphasizes the relationship between the unit circle and the trigonometric functions.

The paragraph further clarifies the connection between the unit circle and trigonometric functions. It explains how the horizontal shift on the unit circle represents the cosine of an angle, while the vertical shift represents the sine. The explanation includes practical examples of calculating cosine and sine values for various angles, reinforcing the concept with visual and numerical information. The paragraph also touches on the periodic nature of these functions, as seen when the angle reaches 360 degrees and returns to its starting point.

This paragraph visually connects the concepts of sine and cosine with the unit circle, transitioning into a discussion on the tangent function. It explains the tangent function as the slope of the line drawn from the center of the unit circle to a point on the circle, which is determined by the angle. The paragraph uses the unit circle to demonstrate how the tangent of an angle is calculated as the ratio of sine to cosine. The explanation includes examples and highlights the undefined nature of the tangent function at 90 degrees due to division by zero.

The paragraph concludes the video script by summarizing the visual understanding of trigonometric functions presented in the video. It emphasizes the practical application of the unit circle in understanding sine, cosine, and tangent, and how this knowledge can enhance the learning experience beyond mere memorization. The speaker expresses hope that the video has been helpful and encourages viewers to subscribe for more content on trigonometry and other mathematical concepts.