Trigonometry 101: Sin, Cos, Tan Made Easy

Welcome to understanding the unit circle, the foundation of trigonometry!Let's start by creating a coordinate plane, where we'll draw our unit circle.The unit circle is special because it has a radius of exactly one unit, and its center is at the origin - the point where x and y equal zero.As we move a point around the unit circle, we can track its x and y coordinates. These coordinates will be crucial for understanding trigonometric functions.A key feature of the unit circle is that it naturally forms right triangles. These triangles are the key to understanding trigonometric relationships.The sides of this right triangle have special relationships that form the basis of trigonometry, which we'll explore in detail in our next lesson.In a right triangle, the sine of an angle is the ratio of the opposite side to the hypotenuse.The opposite side is shown in red, and the hypotenuse, which is always the longest side, is shown in blue.Cosine is the ratio of the adjacent side, shown in green, to the hypotenuse.Tangent is the ratio of the opposite side to the adjacent side, or simply sine divided by cosine.Let's look at the values of these functions for common angles.On the unit circle, the x-coordinate represents cosine of the angle, while the y-coordinate represents sine.Let's start with a helpful memory trick: SOH-CAH-TOA.Here's a real-world example: finding the height of a building using trigonometry.Since we're finding height using an angle and distance, we'll use tangent. The height equals the distance times tangent of thirty degrees.In construction, we often need to find angles between beams or supports.Here are some important tips for using your calculator with trigonometric functions.When solving word problems, knowing which function to use is crucial.Finally, here are the common angle values you should memorize.Let's review what we've learned about applying trigonometry in the real world.Thanks for learning about trigonometry applications with Spark.E!