Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles.

**Trigonometric Functions**

There are six basic trigonometric functions used in Trigonometry. These functions are trigonometric ratios. The six basic trigonometric functions areÂ sine function,Â cosine function, secant function, co-secant function,Â tangent function, andÂ co-tangentÂ function. The trigonometric functions andÂ identitiesÂ are the ratio of sides of a right-angled triangle. The sides of a right triangle are the perpendicular side, hypotenuse, and base, which are used to calculate the sine, cosine, tangent,Â secant,Â cosecant, and cotangent values using trigonometric formulas.

**Unit Circle and Trigonometric Values**

Unit circle can be used to calculate the values of basic trigonometric functions- sine, cosine, and tangent. The following diagram shows how trigonometric ratios sine and cosine can be represented in a unit circle.

**Trigonometric Functions Graph**

The graphs of trigonometric functions have the domain value of Î¸ represented on the horizontal x-axis and the range value represented along the vertical y-axis. The graph of SinÎ¸ passes through the origin and the graph of CosÎ¸ does not pass through the origin. The range of SinÎ¸ and CosÎ¸ is limited to [-1, 1].

Letâ€™s see the practical execution of the trigonometric function graphs of SinÎ¸ and CosÎ¸ using GeoGebra.

Steps for trigonometric function graphs of SinÎ¸:

- Plot two points A and B and draw a unit circle (radius=1cm).
- Mark a point C on the circle and measure angle BAC. Rename the angle as a.
- Change the settings of the x-axis by giving the distance as Ď€/2.
- Draw a line segment between points A and C.
- Now give the input as Segment (C, (x(C),0)).
- A line drawn from C to the x-axis and point C changes with the angle change can be seen.
- Now click on settings and change the line style and colour.
- Now give input as f(x)=sin(x),0<=x<=a.
- A sine wave has drawn as per the given range can be seen.
- Now plot a point on the curve end D.
- Now, to see the change between 0 degrees to 360 degrees, give the input a Â Â Â Â Dynamic coordinate (D, a, y(C)).
- We can see the graph is drawn for every change in angle of BAC and a sine function graph simultaneously.
- Random point E appears along with the curve.
- Now give the input as Segment (E, (x(E),0)).
- Now click on settings and change the line style and colour.
- By clicking on the animation icon, the desired output can be visualized.

The figure shows the sine wave obtained using GeoGebra. It can be observed that the graph of SinÎ¸ passes through the origin.

https://www.geogebra.org/classic/cdkf3rme

Steps for trigonometric function graph of CosÎ¸:

- Plot two points A and B and draw a unit circle (radius=1cm).
- Mark a point C on the circle and measure angle BAC. Rename the angle as a.
- Change the settings of the x-axis by giving the distance as Ď€/2.
- Draw a line segment between points A and C.
- Now give the input as Segment (C, (x(C),0)).
- A line drawn from C to the x-axis and point C changes with the angle change can be seen.
- Now click on settings and change the line style and colour.
- Now give input as f(x)=Cos(x),0<=x<=a.
- A sine wave has drawn as per the given range can be seen.
- Now plot a point on the curve end D.
- Now, to see the change between 0 degrees to 360 degrees, give the input a Dynamic coordinate (D, a, y(C)).
- We can see the graph is drawn for every change in angle of BAC and a sine function graph simultaneously.
- Random point E appears along with the curve.
- Now give the input as Segment (E, (x(E),0)).
- Now click on settings and change the line style and colour.
- By clicking on the animation icon, the desired output can be visualized.

The figure shows the Cosine wave obtained using GeoGebra. It can be observed that the graph of CosÎ¸ does not pass through the origin.

https://www.geogebra.org/classic/bcqtxcjr