Graphs of Trignometric Functions

Trigonometry studies relationships involving the lengths and angles of triangles. The literal use of trigonometry is in three things that are reproductive systems, medical, and procedures developed for geography and astronomy. In geography, sin and cos graphs are used for movement and placement of stars and planet and navigation. sin cos tan graphs are also used extensively in diverse fields such as physics, engineering, chemistry, and mathematics. 

To draw the trigonometry graphs of the function that are sine, cosine, and tangent, we must know the period, amplitude, phase, minimum, and maximum turning points. These graphs are useful in various fields of science and engineering. 

Herewith the help of the corresponding graph, we have explained the graphical representation of sine, cosine, and tangent functions. 


What are Graphs of Trigonometric Functions?

The trigonometry functions are defined by three vital trigonometry ratios: sine, cosine, and tangent. Here you will find the graph of three trigonometry functions, i.e., Sin a, Cos a, and Tan a. In the sin cos tan graph, the radian is the X-axis value of the angles and the y-axis its f(a), has the benefit of function at each given angle.

Graph of Sine (sin) Function

When the sine of an angle is placed against the angle measure, the result will be a classic ““sine curve”” shape.

To draw the sine function, mark the angle along the horizontal x-axis, and for every angle, place the sin of that angle on the vertical y-axis. The result is a smooth curve.

The curves that get this shape are known as ‘‘sinusoidal,’’ after the name of the sine function. When it appears in electronic circuits and radio, the shape is also known as a sine wave. 


The Domain of Sine Function

When you drag point A around, you will notice that after a full rotation about B, the shape of the graph repeats. For each full rotation of the angle, the shape of the sine curve remains the same, and this function is called periodic. The period function is 360 degrees or 2 radians. The point can be rotated multiple times. So no matter how big you can find the sine of any angle. In terms of mathematics, the set of all real numbers is the domain of the sine function.


Range

The set of result values it produces is the range of a function. The sine function ranges from -1 to +1. When you look at the sine wave, you will notice that it never goes out of this range.


Graph of Cosine (cos) Function

When the cos of an angle is placed against the angle measurement, you get a result, which is like the classic shape of a cosine curve.

To draw the cosine function, mark the angle along the horizontal x-axis, and the cosine of that angle will be on the vertical x-axis for every angle. The result will be a smooth curve that varies from +1 to -1. It is the shape like a cosine function but is displaced to the left 90 degrees. The curves that resemble this shape are known as ‘‘sinusoidal’’ after the name of the sine function.


The Domain of Cosine Function

When you drag point A around, you will notice that after a full rotation of B, the shape of the graph repeats. The cosine curve shape is the same for each full rotation of the angle, so the function is called periodic. The period function is 360 degrees or 2 radians. You can rotate the point multiple times. According to mathematics, the domain of the cosine is the set of all real numbers.


Range

A function range is the set of result values it can produce, and the cosine function ranges from -1 to +1. The cosine curve never goes out of this range.


Few similarities between sin and cos graph

  1. Have curves shifted along the x-axis

  2. Have an amplitude of 1        

  3. The same period of 360 degrees

  4. Both have the same domain that is set of all real numbers.


Graph of the Tangent (tan) Function

The Tangent of an angle is placed against that angle measure

To draw the tangent graph, mark the angle along the horizontal x-axis, and for every angle, place the tangent of that angle on the Y-axis. The result is the jagged curve that has positive infinity in one direction and negative infinity in other directions.


The domain of the Tangent Function

It has holes in it. As you stretch the point, A around you will notice that after a full rotation of B, the shape of the graph will repeat. As the tangent curve shape is complete for each full rotation of the angle, the function is known as periodic. Here also, the function period is 360 degrees or 2 radians. 


You can find the tangent of any angle with just one exception; you will see that the tan90 degree is undefined as it requires dividing by zero. Therefore, these angles are not in the domain of the tan function and give undefined results. 

Range


The range of tangent function goes from positive infinity to negative infinity. As infinity is not a real number, the tan 90 degree is undefined 

FAQ (Frequently Asked Questions)

1. What is the period of sine curve?

All trigonometric functions like sin, cos, and tan follow a periodic function. So if we plot them on graphs, what we see is that the shape starts repeating after a certain period. Once the points on the graph complete this one period, the shape of the graph  starts to resemble the start of the same pattern (of course, continuing where it left off). The length of one cycle curve is the period of sine curve. The natural period of the sine curve is 2. So, a coefficient of b=1 is equal to the period of 2. For the period sine curve of any coefficient b, divide 2 by the b coefficient to get the new period of the curve.

2. Does sin or cos start at 0?

The sine function has a beautiful curve that repeats every 360 degrees. It starts at 0, heads up to 1 by /2 radians, and heads down to -1.Since it is possible to calculate sin and cos for a specific real number, these two functions can be easily applied to real numbers. For both sin and cos, the range of these functions must have the interval [-1,1]. If we plot the points on the graph it shows that the first point starts from 0 on x and y axis. In a graph for both sin and cos functions, the shape is repeated after 2π or 360 degree