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Radians quiz #2 Flashcards

Radians quiz #2
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  • Convert the angle 4.54 radians to degrees, rounding to the nearest tenth.
    4.54 radians is approximately 4.54 × (180/π) ≈ 260.1 degrees.
  • What is the approximate degree measure of 1 radian?
    1 radian is approximately 57 degrees. This is a rounded value based on the conversion between radians and degrees.
  • How many radians are there in a full circle?
    A full circle contains 2 pi radians. This is equivalent to 360 degrees.
  • If you go halfway around a circle, how many radians have you traveled?
    Halfway around a circle is pi radians. This is the same as 180 degrees.
  • What is the radian measure for a quarter of a circle?
    A quarter of a circle is pi over 2 radians. This corresponds to 90 degrees.
  • What is the formula to convert degrees to radians?
    To convert degrees to radians, multiply the degree measure by pi over 180. This cancels out degrees and leaves the answer in radians.
  • What is the formula to convert radians to degrees?
    To convert radians to degrees, multiply the radian measure by 180 over pi. This cancels out radians and gives the answer in degrees.
  • Why do you place 180 on the bottom when converting degrees to radians?
    You place 180 on the bottom to cancel out the degree unit. This ensures the result is in radians.
  • What is the radian measure for three-quarters of a circle?
    Three-quarters of a circle is 3 pi over 2 radians. This is equivalent to 270 degrees.
  • When converting 6 pi over 5 radians to degrees, what is the resulting degree measure?
    6 pi over 5 radians converts to 216 degrees. This is found by multiplying by 180 over pi and simplifying.