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Convert the following angle from degrees to radians. Express your answer in simplest form. 510^(@) Answer:

Convert the following angle from degrees to radians. Express your answer in simplest form.\newline510∘ 510^{\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.\newline510∘ 510^{\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 Formula: Now, we apply the formula to 510510 degrees:\newlineRadians = 510×(π/180)510 \times (\pi/180)
  3. Simplify Expression: Simplify the expression by dividing both the numerator and the denominator by their greatest common divisor, which is 3030 in this case:\newlineRadians = (510/30)×(π/(180/30))(510/30) \times (\pi/(180/30))\newlineRadians = 17×(π/6)17 \times (\pi/6)
  4. Final Answer: The expression is now in simplest form, so we have the final answer:\newlineRadians = 17π6\frac{17\pi}{6}

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