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Convert the following angle from degrees to radians. Express your answer in simplest form. 75^(@) Answer:

Convert the following angle from degrees to radians. Express your answer in simplest form.\newline75∘ 75^{\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.\newline75∘ 75^{\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 ×(π/180)\times (\pi/180)
  2. Apply formula: Now, we apply the formula to 7575 degrees: radians=75×(π/180)\text{radians} = 75 \times (\pi/180)
  3. Simplify expression: Simplify the expression by dividing both the numerator and the denominator by their greatest common divisor, which is 1515: \newlineradians=(7515)×(π180/15)\text{radians} = \left(\frac{75}{15}\right) \times \left(\frac{\pi}{180/15}\right)\newlineradians=5×(π12)\text{radians} = 5 \times \left(\frac{\pi}{12}\right)
  4. Final conversion: The expression is now in simplest form, so the conversion is complete: radians=5π12\text{radians} = \frac{5\pi}{12}

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