Unit Circle Solutions for Various Angles

Thread starter Cromulence
Start date Dec 12, 2010
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Circle Unit Unit circle

In summary, the unit circle is a circle with a radius of 1 unit and is centered at the origin on a Cartesian coordinate system. It is completed by plotting points that correspond to specific angles and is used to understand and solve trigonometric equations. The key angles on the unit circle are 0, 30, 45, 60, and 90 degrees, which have special ratios of sine, cosine, and tangent. The unit circle can be applied to solve real-world problems in various fields, such as engineering, physics, and navigation.

Dec 12, 2010

Cromulence

Does anyone know the (x,y) solutions on the unit circle for 15, 75, 105, 165, 195, 255, 285, or 345 degrees?

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Dec 12, 2010

tiny-tim

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Welcome to PF!

Hi Cromulence! Welcome to PF!

Cromulence said:

Does anyone know the (x,y) solutions on the unit circle for 15, 75, 105, 165, 195, 255, 285, or 345 degrees?

Show us what you think …

try 15° first

What is the unit circle and why is it important?

The unit circle is a circle with a radius of 1 unit that is centered at the origin on a Cartesian coordinate plane. It is important because it helps us visualize and understand the properties of trigonometric functions and their relationships to angles and coordinates.

How do you complete the unit circle?

To complete the unit circle, you need to know the coordinates of key points on the circle, which are the x and y-coordinates for angles of 0, 30, 45, 60, and 90 degrees. You can then use these coordinates to plot the points and connect them to form the unit circle.

What are the main trigonometric functions used in completing the unit circle?

The main trigonometric functions used in completing the unit circle are sine, cosine, and tangent. These functions help us determine the coordinates of points on the circle and the relationship between angles and coordinates.

How can completing the unit circle help in solving trigonometric equations?

Completing the unit circle can help in solving trigonometric equations by providing a visual representation of the relationships between angles and coordinates. This can help us understand and apply trigonometric identities and properties to solve equations involving trigonometric functions.

What are some common mistakes to avoid when completing the unit circle?

Some common mistakes to avoid when completing the unit circle include mixing up the coordinates for angles in different quadrants, forgetting to include negative signs for coordinates in certain quadrants, and using incorrect values for the trigonometric functions. It is important to double check your work and use reference angles to avoid these mistakes.