Unit Circle Calculator

The unit circle is a circle centered at the origin, (0, 0) and its radius is 1.The unit circle has all the properties of a circle, and its equation is also derived from the equation of a circle.

What is Unit Circle Calculator?

'Unit Circle Calculator' is an online tool that helps to calculate the sine, cosine, and tangent values. Online Unit Circle Calculator helps you to calculate the sine, cosine, and tangent values in a few seconds.The unit circle is generally represented in the cartesian coordinate plane. The unit circle is algebraically represented using the second-degree equation with two variables x and y.

Unit Circle Calculator

NOTE: Enter an angle in degrees only.

How to Use Unit Circle Calculator?

Please follow the below steps to find the sine, cosine, and tangent values:

• Step 1: Enter the angle of the unit circle in the given input boxes.
• Step 2: Click on the "Calculate" button to find the sine, cosine, and tangent values.
• Step 3: Click on the "Reset" button to clear the fields and enter the different values.

How to Find Unit Circle Calculator?

The general equation of a circle whose center is (x₁, y₁) and whose radius is r is given by the formula:

(​​​​​x - x₁)² + (y - y₁)² = r², Where (x, y) are the coordinates of any point lying on the unit circle.

The unit circle is circle center at origin(0, 0) and radius = 1, then the equation of the unit circle is given by the formula:

(x - 0)² + (y - 0)² = 1²

x² + y² = 1

We calculate the trigonometric functions sine, cosine, and tangent using a unit circle.

From the image, we can calculate trigonometric values for any angle.

sinθ = Opposite / Hypotenuse = y / 1

sinθ = y, sine is y-coordinate

cosθ = Adjacent / Hypotenuse = x / 1

cosθ = x, cosine is x-coordinate

tanθ = Opposite / Adjacent = y / x

tanθ = y / x

Using pythagoras theroem, x² + y² = 1

Therefore, cos²θ + sin²θ = 1

Lets see an example to understand briefly.

Solved Examples on Unit Circle Calculator

Example 1:

Find the trigonometric values if the angle of the unit circle is 45°?

Solution:

sin45° = 1 / √2 = 0.7071

cos45° = 1 / √2 = 0.7071

tan45° = 1

Example 2:

Find the trigonometric values if the angle of the unit circle is 30°?

Solution:

sin30° = 1 / 2 = 0.5

cos30° = √3 / 2 = 0.866

tan30° = 1/√3 = 0.577

Example 3:

Find the trigonometric values if the angle of the unit circle is 60°?

Solution:

sin60° = √3 / 2 = 0.866

cos60° = 1 / 2 = 0.5

tan60° = 1.732

Similarly, you can use the calculator to find the sine, cosine, and tangent values for:

• Angle of unit circle = 60°
• Angle of unit cirlce = 30°

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