Interactive Unit Circle – Explanation, Functions, Solved Examples, and FAQs

# Interactive Unit Circle – Explanation, Functions, Solved Examples, and FAQs

## Define Interactive Unit Circle

The interactive unit circle is a graphical tool that helps users learn and practice basic trigonometric concepts. The unit circle is a circle with a radius of 1, and its center is at the origin (0,0). The unit circle is divided into 360 degrees, with each degree subdivided into 60 minutes. The interactive unit circle displays a small slice of the unit circle, centered on the current cursor position. The user can drag the cursor around the unit circle to change the displayed angle, and can also use the mouse wheel or the up and down arrow keys to change the angle incrementally.

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The interactive unit circle is what that joins the trigonometric function – sine cosine, and tangent, and the unit circle. The unit circle is actually referred to as a circle of radius one suspended in a specific quadrant of the coordinate system. The radius of a unit circle can be taken at any point on the perimeter of the circle.

It forms a right-angled triangle. The angle between this interactive unit circle will be displayed by angle θ. In order to change a grade, you would simply need to click and drag the two control points.

### Functions of Interactive Unit Circle

This unit circle basically consists of 3 functions as follows:

• Sine
• Cosine
• Tangent

The interaction between this unit circle and its correlating functions is referred to as interactive unit circles

### Sine, Cosine and Tangent

1. Sine

The second and another basic trigonometric function is sine represented by θ. In Mathematical terms, sine θ is computed by dividing the perpendicular of a right-angled triangle by its hypotense . Thus, we can compute the length of the sides or the angle of any structure with the help of the above relation. Hence, the formula to calculate Sineθ is as below;

Sine θ = Perpendicular/Hypotenuse

• Cosecant: With respect to cosine, the reciprol of sineθ is referred to as cosecant θ. It is computed by reciprocating sine or just by dividing it with 1. Hence, Cosecant θ = 1/sin θ.
1. Cosine

In a right-angled triangle, the ratio between the base and hypotenuse of a triangle is referred to as cosineθ. It is actually one of the most crucial trigonometric functions of all. In Mathematical terms, cosine is obtained by dividing the base of a right-angled triangle with its hypotenuse. Hence, formula to calculate Cosineθ is as below;

Cosine = Base/Hyp

• Secant: The reciprocal of cosine which is known as secant θ is also used in some triangles The secant θ is used in several numerical calculations and is calculated by reciprocating cosine θ. Thus, Secant = 1/cosine.
1. Tangent

Another and 3rd basic trigonometric function is referred to as tangent. As per sine θ and cosine θ, we can also calculate and get the answer for tangent in a right-angled triangle. In a right triangle, the perpendicular of a triangle is divided with its base, and we easily obtain the value of tangent θ.

The mathematical formula to calculate tangent θ is: Tang θ = Perp/Base.

• Cot: The reciprocal of Tangentθ is known as cot θ. The value of cot can be calculated by reciprocating the value of tangent. The mathematical form of this equation is as stated below: Cot θ = 1/Tang θ.

Thus, all the equations and the trigonometric functions can be understood by the interactive unit circle graph.

## Functions of Interactive Unit Circle

The interactive unit circle is a graphical tool that allows users to explore the properties of circles. It can be used to calculate the coordinates of points on a circle, the length of chords, and the area of sectors. Additionally, the interactive unit circle can be used to explore the relationships between angles and radii, as well as angles and chords.

## Trigonometric Circle Interactive Simulation

In the trigonometric circle interactive simulation, you can change the values of the angles and the radius of the circle. The angles are in radians.

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