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Convert the following angle from degrees to radians. Express your answer in simplest form. 225^(@) Answer:

Convert the following angle from degrees to radians. Express your answer in simplest form.\newline225∘ 225^{\circ} \newlineAnswer:

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Csc, sec, and cot of special anglesright chevron icon

Full solution

Q. Convert the following angle from degrees to radians. Express your answer in simplest form.\newline225∘ 225^{\circ} \newlineAnswer:
  1. Convert to Radians: To convert degrees to radians, we use the conversion factor that π\pi radians is equivalent to 180180 degrees. The conversion formula is:\newlineRadians = Degrees ×(π180)\times \left(\frac{\pi}{180}\right)
  2. Apply Conversion Formula: Now, we apply the formula to 225225 degrees:\newlineRadians = 225×(π/180)225 \times (\pi/180)
  3. Simplify Fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4545 in this case:\newlineRadians = (225/45)×(π/(180/45))(225/45) \times (\pi/(180/45))\newlineRadians = 5×(π/4)5 \times (\pi/4)
  4. Final Radians Value: The simplified form of 225225 degrees in radians is therefore:\newlineRadians = 5π4\frac{5\pi}{4}

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