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Convert the following angle from degrees to radians. Express your answer in simplest form. 495^(@) Answer:

Convert the following angle from degrees to radians. Express your answer in simplest form.\newline495∘ 495^{\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.\newline495∘ 495^{\circ} \newlineAnswer:
  1. Convert to Radians: To convert degrees to radians, we use the conversion factor that π radians is equivalent to 180180 degrees. The formula to convert degrees to radians is:\newlineradians=degrees×π180 \text{radians} = \text{degrees} \times \frac{\pi}{180}
  2. Apply Formula: Now, we apply the formula to 495495 degrees:\newlineradians=495×π180 \text{radians} = 495 \times \frac{\pi}{180}
  3. Simplify Fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1515:\newlineradians=49515×π18015 \text{radians} = \frac{495}{15} \times \frac{\pi}{\frac{180}{15}} \newlineradians=33×π12 \text{radians} = 33 \times \frac{\pi}{12}
  4. Further Simplify Fraction: The fraction 3312 \frac{33}{12} can be further simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 33:\newlineradians=333×π123 \text{radians} = \frac{33}{3} \times \frac{\pi}{\frac{12}{3}} \newlineradians=11×π4 \text{radians} = 11 \times \frac{\pi}{4}

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