The equation x2 + y2 = 1 forms the Circle in Rectangular Coordinate System. This graph is known as Unit Circle it has radius one with the center at its origin i.e. (0, 0). The Domain of the trigonometric function is the Set of angles and their ranges are the set of real Numbers. Circular Functions are defined in a way such that Sets of angles are domain which correspond to the measures of the angles of the analogous trigonometric function, like in analog Trigonometry the range of these Trigonometric Functions are also the set of Real Numbers and these type of functions are termed as Circular Functions, here the Radian Measure of angle is determined by the length of arc of circle. In other words when Trigonometric Functions are defined using unit circle then they directly head towards these graphs of the circular functions.
Lets plot the Graphs of Circular Functions with unit circle equation x2 + y2 = 1 as we can see in the figure:
Point A (1, 0) is located at the Intersection of x - axis and of the unit circle. Let ‘q’ be the real number. Graphing circular functions is done by Initiating from Point ‘A’ and measuring │q│ units along the unit of the circle in anti clockwise direction. Here q > 0 and in clockwise direction if q < 0 and it ends up at point p(x, y). So other remaining circular function such as Tangent, cotangent, secant, cosecant can be defined in the terms of sine and cosine.
Sin q = y,
cos q = x,
Therefore rest of the functions will be:
tan q = sin q/ cos q ; cos q ≠ 0,
cot q = cos q / sin q ; sin q ≠ 0,
sec q = 1/ cos q ; cos q ≠ 0,
cosec q = 1/ sin q ; sin q ≠ 0.
There are different types of the graphs which we study under the subject of the Math especially in the topic of the Trigonometry for example the graph of the sine function, the graph of the cosine function, the graph of the Tangent function and also the graphs of the Logarithm function and the Exponential Function and many other graphs. It is very importan...Read More
It is very common for us to study about the different Types of Graph in Math. Especially very frequently we come across various types of graphs of different kinds of trigonometric Functions. For example, the graphs of the functions like sine function, tangent function and cosine function are the ones on which we usually pay much of the attention because the ...Read More
First of all lets go through sine and cosine function and then we will see steps to graph a basic sine or cosine function. A sine function is basically a function which is a function of angle. It is related to the sides of triangle and angles of a Right Triangle. Let us take a a Right Angle triangle with base AB , Height BC and Hypotenuse A...Read More
Graphs of sine and cosine Functions can be used in plotting daily temperature in a year, in Graphing the cyclic commodity prices, in finding the heart beat rates on the ECG machines. The graph of Sine and cosine functions can be plotted easily. Sine function is a function used to model any periodic phenomenon which can be of sound waves, intensity of ...Read More
A circular or periodic function F (X) can be defined as a function in which for every real number 'X' in the Domain of F (X), every Integer 'N', and some positive real number 'P'. Smallest possible value of 'P' represents the Period of function. Graphs of basic circular Functions can be drawn as follows:
Graph of sine function can be drawn as follows:...Read More
Six Trigonometric Functions are: sine, cosine, tangent, cotangent, secant and cosecant. Their corresponding inverse functions can be written as arc sine, arc cosine, arc Tangent, arc cotangent, arc secant and arc cosecant. These functions are also periodic in nature. Graphs of inverse Circular Functions can be drawn as follows:
1. Graph of a...Read More
Sine and cosine Functions are Circular Functions or we can say they are trigonometric functions. Here we will discuss Changes in Sine and Cosine Functions. Sine function is a trigonometric Ratio which i...Read More