### Images and properties of six trigonometric functions

The six trigonometric functions are cosine, cosine, tangent, cotangent, secant, and cosecant. In mathematical analysis, trigonometric functions are also defined as solutions of infinite series or special differential equations, allowing their assignments to expand to arbitrary real-labeled values and even complex labeled values.

Trigonometric functions in detail:

1. Sine function

Format: sin(θ).

Effect: in a right triangle, the ratio of the length of the opposite side of the angle of size θ (the enterprise is the inclination) over the length of the arc of the circle, the value of the function is the ratio of the said ratio, but also the last of csc (θ).

Function image: waveform graph.

Value range: -1 to 1.

2. Cosine function

Format: cos (θ).

Effect: in a right triangle, the ratio of the length of the neighboring side of the angle of size (the enterprise is the inclination) to the length of the arc of the circle, the value of the function is the ratio of the said ratio, but also the last of sec (θ).

Image of the function: waveform graph.

Value range: -1 to 1.

3. Tangent function

Format: tan (θ).

Effect: in a right triangle, the ratio of the length of the opposite side of the angle of size θ (the enterprise is the degree of inclination) neighboring the length of the side to find the value of the function is the ratio of the said ratio, but also the last of the cot (θ).

Functional image: the following graphic plane diagram right-angled coordinate system embodied.

Value range: -∞~∞.

4. Cotangent function

Format: cot (θ).

Efficacy: in right triangles, the ratio of the lengths of the sides adjacent to the angle of size θ (the enterprise is the inclination) kernel to the length of the side to find the value of the function is the ratio of the said ratio, but also the last of tan (θ).

Functional image: the following graphic plane diagram right-angled coordinate system embodied.

Value range: -∞~∞.