Lesson Overview:

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a. Finding the Exact Value of Degrees Without the Unit Circle

b. Finding the Exact Value of Radians Without the Unit Circle

c. Converting between Degrees and Radians.

d. Finding co-terminal angles

Part A: Finding the Exact Value of Degrees 

You can use your knowledge of the unit circle to solve for the value of any given degree measure for both major and minor function. Depending of the circumstances of the problem your process may be a little different.

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Here are some key rules to remember to make the conversion process easier.

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Here is an example on how to find the exact value of degrees for major functions:

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Here is an example on how to find the exact value of degrees for minor functions:

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Part B: Finding the Exact Value of Radians

You can use your knowledge of the unit circle to solve for the value of any given radian for both major and minor function. Depending of the circumstances of the problem your process may be a little different.

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Here are some key pieces of information to keep in mind that will make the process easier.

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Here is an Example on how to find radian measures for major functions:

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Here is an Example on how to find radian measures for minor functions:

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Part C: Converting between Degrees and Radians.

To convert between degrees and radians you must know two formulas and when to use each one of these formulas.

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Here are the two formulas you must know:

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Here is an example to convert from a degree to a radian:

 

 

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Here is an example to convert from a radian to a degree:

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Part D: Finding co-terminal angles

To solve for the positive and negative conterminal angles you must add or subtract in increments of 360 degrees. If you have a negative angle draw it in a clockwise rotation, and if you have a positive angle draw it in a counterclockwise direction.

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Here is a chart with information that will help you when working on conterminal angles.

           

 

 

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Here is an example on how to solve for co-terminal angles:

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Radians and the Unit Circle on the SAT

 

 

 

 

 

 

 

 

 

 

 

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Radians and the Unit Circle Real World

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Conclusion:

You should be able to find the exact value of degrees and radians based on the information you know about the unit circle and the rules that go along with each quadrant. You should also be able to convert between degrees and radians using the two given formulas. Lastly, you should be able to solve for co-terminal angles.