A wheel rotates through an angle of straight pi over 30 radians in one second. How many revolutions will it make in 5 minutes?


Radian measure of an angle turned in one second  = open parentheses straight pi over 30 close parentheses to the power of straight c

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∴  Number of revolutions in one second = 6 over 360 space equals space 1 over 60

  Hence, the number of revolutions in 5 minutes  = space space 1 over 60 space cross times space 60 space cross times space 5 space equals space 5

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“Express in radians the angle 50° 37’ 30” .

30 to the power of apostrophe apostrophe end exponent space equals space open parentheses 30 over 60 close parentheses to the power of apostrophe space equals space open parentheses 1 half close parentheses to the power of apostrophe

37 apostrophe 30 apostrophe apostrophe space equals space open parentheses 37 plus 1 half close parentheses to the power of apostrophe space equals space open parentheses 75 over 2 close parentheses to the power of apostrophe space equals space open parentheses fraction numerator 75 over denominator 2 cross times 60 end fraction close parentheses to the power of ring operator space equals space open parentheses 5 over 8 close parentheses to the power of ring operator
50 to the power of ring operator 37 apostrophe 30 apostrophe apostrophe space equals space open parentheses 50 plus 5 over 8 close parentheses to the power of ring operator space equals space open parentheses 405 over 8 close parentheses to the power of ring operator

       open parentheses 405 over 8 close parentheses to the power of ring operator space equals space straight pi over 180 cross times 405 over 8 space space radians space equals space fraction numerator 9 straight pi over denominator 32 end fraction space radians
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Convert straight pi over 12 to degrees.


Radians to degrees: multiply by space space 180 over straight pi

∴          straight pi over 12 space radians space equals space open parentheses straight pi over 12 cross times 180 over straight pi close parentheses to the power of degree space equals space 15 degree

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Convert negative 60 degree to radians


Degrees to radians: multiply by straight pi over 180

∴          negative 60 degree space equals space open parentheses negative 60 space cross times space straight pi over 180 close parentheses space radians space equals space minus straight pi over 3 space space radians

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Find 1 radian angle in degrees, minutes, seconds.

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