mathematicsnotes386

muaz ? ? ?   Trigonometry is a branch of mathematics that deals with the study of relationships between the angles and sides of triangles, as well as the trigonometric functions associated with those angles. It has extensive applications in various fields such as physics, engineering, astronomy, architecture, and more. Here are some key concepts and components of trigonometry: Angles: Trigonometry primarily deals with angles. An angle is formed when two rays originate from a common endpoint, known as the vertex. Angles are typically measured in degrees or radians. Right Triangle Trigonometry: In a right triangle, which is a triangle with one angle equal to 90 degrees, trigonometric functions such as sine, cosine, and tangent are defined based on the ratios of the lengths of the sides of the triangle. These ratios provide important relationships between the angles and sides of the triangle. Trigonometric Functions: Sine (sin): In a right triangle, the sine of an angle is...

  The domains of trigonometric functions and fundamental identities depend on the specific function or identity being considered. Here's a brief overview: Domains of Trigonometric Functions: Sine Function (sin(x)): The domain of the sine function is all real numbers. In other words, you can input any real number into the sine function and get a valid output. Cosine Function (cos(x)): Similar to the sine function, the domain of the cosine function is also all real numbers. Tangent Function (tan(x)): The tangent function is undefined at odd multiples of π/2 (e.g., π/2, 3π/2, -π/2, etc.) because at these points, cosine is zero, making the fraction undefined. Therefore, the domain of the tangent function is all real numbers excluding odd multiples of π/2. Cosecant Function (csc(x)): The cosecant function is the reciprocal of the sine function, so it is undefined wherever sine is zero. Therefore...