Enter the angle of the unit circle into the calculator. The calculator will display the corresponding sine, cosine, and tangent values of the unit circle associated with those values.

Unit Circle Formula

The following formula is used to calculate the values of a unit circle.

Sin (X) = X

Cosine (X) = Z

Tangent (X) = W

Where x is the angle and y, z and w are the values of the unit circle.

To calculate a unit circle, take the sine, cosine, and tangent of the angle to get the X, Y, and Z coordinates respectively.

Unit Circle Definitoin

A unit circle is defined as any circle with a radius of 1 unit.

How to memorize a unit circle?

The best way to memorize a unit circle is to remember that sin is X, cosine is y, and tan is z. Add that to the factor that the unit circle always has a radius of 1 and you can determine your unit circle.

What is it called unit circle?

The unit circle is called such because the radius of the circle is a unit of 1, or magnitude of 1. That is one unit, hence the name unit circle.

Why are unit circles important?

Just like with a unit vector, unit circles are important for simplifying problems with large numbers. If you can simply a problem down to a unit circle with a radius of 1, then you can compare the values of circles with drastically different sizes.

How to calculate a unit circle?

How to calculate a unit circle

  1. First, measure the angle of the unit circle.

    This is the angle measure from the positive x axis.

  2. Calculate the value of sine (X)

    This value will be equal to the Y portion of the triangle encapsulated.

  3. Calculate the value of cosine (X)

    This will be equal to the x portion of the triangle.

  4. Calculate the value of tangent of (X)

    This is equal to the value of the hypotenuse.

FAQ

What is a unit circle?

A unit circle is a circle with a radius of 1. It’s also closely related to a unit vector which is a vector with a magnitude of 1, however, it is no the same.

How can a unit circle be used?

A unit circle is used in order to simplify a problem down to a smaller scale, of 1 to be exact. In other words, it’s reducing a large circle value to one with a radius of 1.