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If x^(@) is equal to 7pi radians, what is the value of x ? (The number of degrees of arc in a circle is 360 . The number of radians of arc in a circle is 2pi.)

If x∘ x^{\circ} is equal to 7π 7 \pi radians, what is the value of x x ?\newline(The number of degrees of arc in a circle is 360360 . The number of radians of arc in a circle is 2π 2 \pi .)

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Full solution

Q. If x∘ x^{\circ} is equal to 7π 7 \pi radians, what is the value of x x ?\newline(The number of degrees of arc in a circle is 360360 . The number of radians of arc in a circle is 2π 2 \pi .)
  1. Convert Radians to Degrees: To convert radians to degrees, we use the relationship that 2π2\pi radians is equal to 360360 degrees. Since we are given that x^{(\@)} is equal to 7π7\pi radians, we need to find out how many degrees that is.
  2. Set Up Proportion: We set up the proportion to convert 7π7\pi radians to degrees: (7π radians)×(360 degrees/2π radians)(7\pi \text{ radians}) \times (360 \text{ degrees} / 2\pi \text{ radians}). The π\pi radians cancel out, leaving us with the calculation 7×(360/2)7 \times (360 / 2).
  3. Perform Calculation: Performing the calculation, we get 7×1807 \times 180, which equals 12601260 degrees. This is the value of x^{(\@)} in degrees.
  4. Final Value of x: Since x(@)x^{(@)} represents the angle in degrees, the value of xx is simply 12601260 degrees. There is no further calculation needed.

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