Unit Circle - Trigonometry

The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. is equivalent to which corresponds to the point on the unit circle.

The angle or corresponds to the point .

In order to find the point corresponds to the angle on the unit circle we can write:

In the unit circle which has the radious of we can write:

So the point corresponds to the angle on the unit circle is

The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. is equivalent to which corresponds to the point on the unit circle.

The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. is a full circle plus a more. So, the angle corresponds to the point on the unit circle.

For a point to be on the unit circle, it has to have a radius of one. Therefore, the sum of the squares of point's coordinates must also equal one.

Let's try the point .

Therefore, this point is not on the unit circle.

The coordinates of the point on the circle for each angle are .

Since and , the point will be .

By definition, the radius of the unit circle is 1.

The unit circle must have a radius of 1.

Use the circular area formula to find the area.

The only values such that

are at the values:

This means that the only choice for is . or achieve the necessary angles to satisfy this trigonometric ratio.

The tangent of an angle yields the ratio of the opposite side to the adjacent side.

If this ratio is , we can see that this is a Pythagorean triple (3-4-5); the absolute value of the sine of this angle would be .

However, the question indicates that this angle lies in the 3rd quadrant. The sine of any angle in the 3rd or 4th quadrant is negative, since it is equivalent to the y-coordinate of the corresponding point on the unit circle.

Therefore,

.

On the unit circle, the cosine of an angle yields the x-coordinate.

There are two angles at which the _x-_coordinate on the unit circle is : and .

is coterminal with , and is coterminal with .

is in the 4th quadrant, and has a positive x-coordinate.

Step 1: Define a Unit Circle:

A unit circle is used in Trigonometry to draw and describe distinct angles. The unit circle works along with the coordinate grid.

Step 2: There are quadrants in the coordinate grid, each quadrant can fit degrees.

Step 3: Multiply how many degrees in quadrant by .. to get the full unit circle:

The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. radians is equivalent to . This is a full circle plus a quarter-turn more. So, the angle corresponds to the point on the unit circle.

The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. is equivalent to which corresponds to the point on the unit circle.

The angle or corresponds to the point .

In order to find the point corresponds to the angle on the unit circle we can write:

In the unit circle which has the radious of we can write:

So the point corresponds to the angle on the unit circle is

The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. is equivalent to which corresponds to the point on the unit circle.

The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. is a full circle plus a more. So, the angle corresponds to the point on the unit circle.