Graph, Domain, and Range of Trigonometric Functions:

Trigonometric functions are mathematical functions that relate the angles of a triangle to the ratios of the sides. The most commonly used trigonometric functions include sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Understanding the graphs, domains, and ranges of these functions is crucial in many areas of mathematics and physics. Let's explore each trigonometric function individually:

Sine Function (sin):
The sine function relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of the hypotenuse. The graph of the sine function is a periodic wave that oscillates between -1 and 1. The key points to note are:

- Graph: The graph of the sine function starts at (0, 0) and oscillates between -1 and 1. It repeats itself every 2π radians or 360 degrees.

- Domain: The domain of the sine function is all real numbers since the angle can take any value.

- Range: The range of the sine function is between -1 and 1, inclusive. It can be expressed as [-1, 1].

Cosine Function (cos):
The cosine function relates the angle of a right triangle to the ratio of the length of the adjacent side to the length of the hypotenuse. The graph of the cosine function is also a periodic wave that oscillates between -1 and 1. The key points to note are:

- Graph: The graph of the cosine function starts at (0, 1) and oscillates between -1 and 1. It also repeats itself every 2π radians or 360 degrees, just like the sine function.

- Domain: The domain of the cosine function is all real numbers since the angle can take any value.

- Range: The range of the cosine function is also between -1 and 1, inclusive. It can be expressed as [-1, 1].

Tangent Function (tan):
The tangent function relates the angle of a right triangle to the ratio of the length of the opposite side to the length of the adjacent side. The graph of the tangent function consists of repeating vertical lines called asymptotes and periodic waves between the asymptotes. The key points to note are:

- Graph: The graph of the tangent function has vertical asymptotes at odd multiples of π/2. It repeats itself every π radians or 180 degrees.

- Domain: The domain of the tangent function is all real numbers except for the values where there are vertical asymptotes. Therefore, the domain can be expressed as (-∞, -π/2) U (-π/2, π/2) U (π/2, 3π/2) U (3π/2, ∞).

- Range: The range of the tangent function is all real numbers since the ratio of the opposite and adjacent sides can take any value.

Cosecant Function (csc):
The cosecant function is the reciprocal of the sine function,