Trigonometry : Radians and Conversions

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Example Questions

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Example Question #51 : Radians And Conversions

Convert  radians into degrees.

Possible Answers:

Correct answer:

Explanation:

Recall the definition of "radians" derived from the unit circle:

The quantity of radians given in the problem is . All that is required to convert this measure into degrees is to denote the unknown angle measure in degrees by  and set up a proportion equation using the aforementioned definition relating radians to degrees:

Cross-multiply the denominators in these fractions to obtain:

or

.

Canceling like terms in these equations yields

Hence, the correct angle measure of  in degrees is .

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