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Which of the following radian measures is equal to 135^(@) ? Choose 1 answer: (A) (pi)/(4) radians (B) (pi)/(2) radians (C) (3pi)/(4) radians (D) pi radians

Which of the following radian measures is equal to 135∘ 135^{\circ} ?\newlineChoose 11 answer:\newline(A) π4 \frac{\pi}{4} radians\newline(B) π2 \frac{\pi}{2} radians\newline(C) 3π4 \frac{3 \pi}{4} radians\newline(D) π \pi radians

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Full solution

Q. Which of the following radian measures is equal to 135∘ 135^{\circ} ?\newlineChoose 11 answer:\newline(A) π4 \frac{\pi}{4} radians\newline(B) π2 \frac{\pi}{2} radians\newline(C) 3π4 \frac{3 \pi}{4} radians\newline(D) π \pi radians
  1. Identify formula for conversion: Identify the formula to convert degrees to radians. The formula is radians=degrees×(π180∘)\text{radians} = \text{degrees} \times \left(\frac{\pi}{180^\circ}\right).
  2. Convert 135135 degrees to radians: Convert 135135 degrees into radians using the formula. By substituting 135135 degrees into the formula, we get 135∘×(π180∘)=(135180)×π=(34)×π=(3π4)135^\circ \times \left(\frac{\pi}{180^\circ}\right) = \left(\frac{135}{180}\right) \times \pi = \left(\frac{3}{4}\right) \times \pi = \left(\frac{3\pi}{4}\right) radians.
  3. Match result with options: Match the result with the given options. The correct option that matches (3π4)(\frac{3\pi}{4}) radians is option (C).

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