Uses of graph in trigonometry

It can be said that graphs are used in almost every study of science and engineering. It has been observed from the studies that trigonometry is used mainly to study the relationship between the angles of the triangles and the lengths. It can be further argued that the literal use of graphs in trigonometry is in three different types of studies which are medical, reductive systems and in the procedures of developing astronomy and geography. The functions of trigonometry can be explained as the three vital ratios of trigonometry which are: sine, cosine and tangent. It can be further argued that the graph in trigonometry is used to represent these three ratios. 

Discussion

Importance of graph in trigonometry 

It can be further said that the advantage of using graphs is that they can represent general tendencies for evaluating the quantitative behavior of data. It can be said that graphs are done to serve a predictive function. However, the graphing of the variables and the representation can be also inaccurate and often misleading. It has been observed from the studies that graphs are used to employ two different axes which are vertical axes and horizontal axes. It can be said that the horizontal axes represent the set of independent variables. However, the vertical axes are used to represent the set of dependent variables. It can be further argued that the most common graph which is generally used in trigonometry is the broken line graph. 

Different types of graphs in trigonometry 

Graph of sine function  

It has been observed from the studies that when the sine of a specific angle is used against the angle measure, it can be said that the result will come out as a classic “sine curve” in a shape. 

Graph of the tangent function 

It can be said that the graph is used when the tangent of any angle is put against the angle measure. It has been observed that the tangent graph is mainly drawn from the horizontal x-axis. However, for every other angle, the tangent is placed on the y-axis. 

Graph of the Cosine function 

The graph is used here when the cos of any angle is put against the measurement of an angle, and that is when the result will be like the classic shape of a cosine curve. 

Period and Amplitude 

It has been observed from the studies that period is explained as the distance between the two maximum points or minimum points which also has to be consecutive in nature. It also implies that the distance has to be equal. While graphing the variables, the period goes from one peak to another peak. In the below equation, the value of A is equal to 1, B is equal to 1, C is equal to 0 and D is equal to 0. However, it can be said according to the calculations that the value of period a\for this equation will be 2π and the value of amplitude will be equal to 1. It can be further argued that there would not be any vertical shift or phase shift. 

Example: y = A sin B(x + C)) + D 

The amplitude can be explained as the vertical distance, which is between the midline, and it is one of the extremism points. The graphing of the variables is however possible with changes in the amplitude and period for both the sine function and the cosine function. 

Importance of graphs 

Graph

The main purpose of the graph is to illustrate data relationships visually. It is important for representing complicated or numerous data in less space and text adequately. Additionally, it values a large set of data, which is effective to help the users in understanding the quantitative variables in a better manner.

Main purposes of chart and graphs 

It can be said that the chart can be used in the form of a diagram or a graph. However, the datasets can be represented by transforming them into a meaningful display of quantitative information with the help of charts.  It has been observed from the studies that there are different types of charts such as “Histogram, Historical Bar Chart, Line Chart, Stacked Bar Charts, Pie charts in excel, Vertical Bar Charts and area charts in excel”. Mainly people used charts and graphs for demonstrating relationship, pattern and trends between data sets. It can be further argued that different types of charts are widely used in business as it simplifies the data and analyzes formats.

Conclusion

It can be considered that a graph is used in trigonometry just as the pictorial representation of the statistical data. The main function of graphing is to draw a pattern or find out a relationship between the different variables. The graphs are mainly used to represent the trigonometry functions which are sine, cosine and tangent. In order to achieve accurate results from the graphs, it is important to understand the period and amplitude. It can be said that a graph is a pictorial representation showing general tendencies for the quantitative behavior of the data. Graph can also have a relationship with the charts as it is a type of chart that is used to show the mathematical relationship between different sets of data.