What is trigonometry and how to understand it and how it is used in real worls

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Trigonometry is a branch of mathematics that studies the relationships between angles and sides in triangles. It uses special functions called sine, cosine, and tangent to describe these relationships. In a right triangle, we have three sides: the hypotenuse, which is the longest side opposite the right angle, the adjacent side next to our angle theta, and the opposite side across from our angle. The three basic trigonometric functions are sine, cosine, and tangent. Sine of theta equals the opposite side divided by the hypotenuse. Cosine of theta equals the adjacent side divided by the hypotenuse. And tangent of theta equals the opposite side divided by the adjacent side. A helpful way to remember these is the mnemonic SOH CAH TOA, which stands for Sine equals Opposite over Hypotenuse, Cosine equals Adjacent over Hypotenuse, and Tangent equals Opposite over Adjacent. The unit circle is a powerful tool for understanding trigonometry. It's a circle with radius 1 centered at the origin of a coordinate system. For any angle theta, the coordinates of the point where the angle intersects the unit circle are cosine theta and sine theta. This allows us to extend trigonometry beyond right triangles to work with any angle, including angles greater than 90 degrees.