Unlocking the Secrets of the Unit Circle: How to Find Missing Coordinates Using Trigonometry

missing coordinate on unit circle

x² + y² = 1

The unit circle is a circle with a radius of one, centered at the origin of a coordinate plane. It is used to help understand the properties of trigonometric functions. The circle is divided into four quadrants, each of which corresponds to different signs of the sine, cosine, and tangent functions.

To find a missing coordinate on the unit circle, you can use the Pythagorean theorem to determine the length of the missing side of a right triangle. For example, if you know the value of one of the coordinates, like the x-coordinate, and you need to find the y-coordinate, you can use the formula:

y = ±sqrt(1 – x^2)

The ± sign accounts for the fact that the y-coordinate can be either positive or negative, depending on which quadrant the point is located in.

Similarly, if you know the value of the y-coordinate and need to find the x-coordinate, you can use the formula:

x = ±sqrt(1 – y^2)

Again, the ± sign takes into account the sign of the x-coordinate in different quadrants.

It’s important to remember that the coordinates on the unit circle are specific ratios of the sides of a right triangle, and can be found using trigonometric functions like sine, cosine, and tangent. So if you know an angle and one of the coordinates on the unit circle, you can use trigonometry to find the missing coordinate.

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