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Convert the following angle from degrees to radians. Express your answer in simplest form. 270^(@) Answer:

Convert the following angle from degrees to radians. Express your answer in simplest form.\newline270∘ 270^{\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.\newline270∘ 270^{\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. Therefore, to convert 270270 degrees to radians, we multiply 270270 degrees by the conversion factor (π/180)(\pi/180).
  2. Perform Multiplication: Perform the multiplication to find the radian measure: 270270 degrees ×(π180)=(270180)×π=(32)×π\times \left(\frac{\pi}{180}\right) = \left(\frac{270}{180}\right) \times \pi = \left(\frac{3}{2}\right) \times \pi.
  3. Simplify Fraction: Simplify the fraction 270180\frac{270}{180} by dividing both the numerator and the denominator by their greatest common divisor, which is 9090. This gives us (27090)/(18090)=32\left(\frac{270}{90}\right)/\left(\frac{180}{90}\right) = \frac{3}{2}.
  4. Final Radian Measure: Now, we have the simplified fraction (32)×π(\frac{3}{2}) \times \pi, which is the radian measure of 270270 degrees.

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