Unit Circle Calculator

Calculate Unit Circle Values

Formula

To calculate the values of a unit circle:

\[ \sin(X) = \sin(\theta) \]

\[ \cos(X) = \cos(\theta) \]

\[ \tan(X) = \tan(\theta) \]

Where:

What is a Unit Circle?

A unit circle is defined as any circle with a radius of 1 unit. It is commonly used in trigonometry to define the sine, cosine, and tangent functions for all real numbers.

Example Calculation 1

Let's assume the following value:

Using the formula:

\[ \sin(45^\circ) = \sin\left(\frac{\pi}{4}\right) \approx 0.7071 \]

\[ \cos(45^\circ) = \cos\left(\frac{\pi}{4}\right) \approx 0.7071 \]

\[ \tan(45^\circ) = \tan\left(\frac{\pi}{4}\right) \approx 1 \]

The sine, cosine, and tangent values are approximately 0.7071, 0.7071, and 1, respectively.

Example Calculation 2

Let's assume the following value:

Using the formula:

\[ \sin(90^\circ) = \sin\left(\frac{\pi}{2}\right) = 1 \]

\[ \cos(90^\circ) = \cos\left(\frac{\pi}{2}\right) = 0 \]

\[ \tan(90^\circ) = \tan\left(\frac{\pi}{2}\right) \text{ is undefined} \]

The sine, cosine, and tangent values are 1, 0, and undefined, respectively.