Description Of Graphs Of T Ratios

To determine the graph of a trigonometric function, you should be familiar with the period amplitude-phase minimum and maximum of the trigonometric function. Graphs of trigonometric functions hold Central importance with versatile use in several engineering and science branches. This article will deliver information with a comprehensive guide to the description of graphs of the trigonometric function. The graphical representation of trigonometric functions will be explained in this article with the help of corresponding graphs. There are three important trigonometric functions: sine, cosine, and tangent. These three trigonometric functions are important and used to derive the graph of the other three circular functions.

Graphs of trigonometric functions

There are three important trigonometric ratios: sin, cos, and tan. The functions are defined based on these trigonometric ratios. Based on the functions, the graphs of these trigonometric functions are determined with the basic structure of x-axis values of angles. The y-axis determines the value of that particular function at a corresponding angle.

Now that you have understood the concept of graphs of trigonometric functions. Let us move forward with the graph of each trigonometric ratio.

Sine graph 

• The function is determined as y= sin x 

• The multiples of π determine the roots or zeros of the function

• As sin x equals zero, the graph passes through the x-axis at X = 0

• The sign function has a period of 2π

• The curve’s height determines the value of the function at the particular value of the angle.

• The maximum value of sin = 1 and the minimum value of sin = -1

Cosine graph 

• The function is determined as y = cos x

• The graph of cos x is determined by shifting the graph of sin x by 2 to the left.

• The cosine function has a period of 2π.

• The graph can determine the maximum value of the cosine function as 1

• The graph can determine the minimum value of the core sin function as -1

Similarities between sine and cosine graph

There are three similarities between the cosine and sine graphs:

The curve with which the graph is shifted along the x-axis is the same

Both cosine & sine graphs have the same amplitude of 1

The period of cosine & sine graphs is the same as 2π

Tangent graph 

The tangent function is different from the cosine and sine functions. The graph of the tangent function goes between positive and negative infinity, crossing the axis 0 with a period of π

• The function of the tangent graph is determined by y= tan x

• The amplitude of the graph is undefined as the values tend to infinity

• The period of the tangent graph is also 2π

Now that you have understood the graph of three important trigonometric functions. Let us understand the key concepts required to draw the graph of trigonometric functions. 

You must understand three important concepts to draw the graph of any trigonometric function. These concepts are:

• Amplitude

• Period 

• Phase

Let us understand each in detail:

Amplitude

Amplitude is defined as the absolute value of some number multiplied by the trigonometric function. It is also determined as the height from the axis line to the graph’s peak. This can also be determined by calculating the height between the highest and lowest points of the graph divided by 2. The physical significance of amplitude is that it tells about the curve’s height.

Period 

A period can be defined as any value from one peak to another graph’s peak. Period helps us understand the repetition of the curve on the graph.

Phase 

The graph phase determines function shifting from the usual position when shifted horizontally. Here are some key terms related to the phase of a graph of trigonometric functions:

It determines the maximum and minimum turning points.

Conclusion

The graph of trigonometric functions is used to determine several key concepts of a trigonometric function, including the period and phase. These concepts of trigonometric ratios are important to determine the use of that particular trigonometric ratio or trigonometric function in respective scenarios. To draw the graph of any trigonometric function, you have to transform the trigonometric function into the general equation or general form of the trigonometric function equation. This transformation will help determine the graph’s amplitude, period, and phase. These values are the first step in drawing the graph of trigonometric functions. This article has delivered an informative concept of graphs of trigonometric functions.