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If theta=225^(@), what is the value of theta in radians? Choose 1 answer: (A) (4pi)/(3) (B) (5pi)/(4) (C) (2pi)/(5) (D) (7pi)/(6)

If θ=225∘\theta=225^{\circ}, what is the value of θ\theta in radians?\newlineChoose 11 answer:\newline(A) 4π3\frac{4\pi}{3}\newline(B) 5π4\frac{5\pi}{4}\newline(C) 2π5\frac{2\pi}{5}\newline(D) 7π6\frac{7\pi}{6}

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Full solution

Q. If θ=225∘\theta=225^{\circ}, what is the value of θ\theta in radians?\newlineChoose 11 answer:\newline(A) 4π3\frac{4\pi}{3}\newline(B) 5π4\frac{5\pi}{4}\newline(C) 2π5\frac{2\pi}{5}\newline(D) 7π6\frac{7\pi}{6}
  1. Identify formula: 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 degrees to radians: Convert 225225 degrees into radians using the formula. By substituting 225225 degrees into the formula, we get 225∘×(π/180∘)=(225/180)×π=(5/4)×π=5π/4225^\circ \times (\pi/180^\circ) = (225/180) \times \pi = (5/4) \times \pi = 5\pi/4 radians.
  3. Match radians value: Match the calculated radians value to the correct option. The calculated value is 5π/45\pi/4 radians, which corresponds to option (B)(B).
  4. Confirm correctness: Confirm that there are no mathematical errors in the previous steps and that the conversion from degrees to radians was done correctly.

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