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Convert the angle (5pi)/(4) radians to degrees. Answer:

Convert the angle 5π4 \frac{5 \pi}{4} radians to degrees.\newlineAnswer:

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Full solution

Q. Convert the angle 5π4 \frac{5 \pi}{4} radians to degrees.\newlineAnswer:
  1. Convert to degrees: To convert radians to degrees, we use the conversion factor that π\pi radians is equal to 180180 degrees. The formula to convert an angle in radians to degrees is: degrees=radians×(180/π)\text{degrees} = \text{radians} \times (180/\pi).
  2. Apply formula: Now, we apply the formula to the given angle (5π)/(4)(5\pi)/(4) radians: degrees = (5π)/(4)×(180/π)(5\pi)/(4) \times (180/\pi).
  3. Simplify expression: We can simplify the expression by canceling out the pi terms: degrees=54×180\text{degrees} = \frac{5}{4} \times 180.
  4. Calculate degree measure: Multiplying 54\frac{5}{4} by 180180 gives us the degree measure: degrees = 5×45=2255 \times 45 = 225 degrees.

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