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If theta=(pi)/(2) radians, which of the following shows the measure of theta in degrees? Choose 1 answer: (A) 45^(@) (B) 90^(@) (c) 135^(@) (D) 180^(@)

If θ=π2 \theta=\frac{\pi}{2} radians, which of the following shows the measure of θ \theta in degrees?\newlineChoose 11 answer:\newline(A) 45∘ 45^{\circ} \newline(B) 90∘ 90^{\circ} \newline(C) 135∘ 135^{\circ} \newline(D) 180∘ 180^{\circ}

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Full solution

Q. If θ=π2 \theta=\frac{\pi}{2} radians, which of the following shows the measure of θ \theta in degrees?\newlineChoose 11 answer:\newline(A) 45∘ 45^{\circ} \newline(B) 90∘ 90^{\circ} \newline(C) 135∘ 135^{\circ} \newline(D) 180∘ 180^{\circ}
  1. Identify relationship between radians and degrees: Identify the relationship between radians and degrees. One radian is equal to 180π\frac{180}{\pi} degrees.
  2. Convert radians to degrees: Convert θ\theta from radians to degrees using the relationship from the previous step. Since θ=π2\theta = \frac{\pi}{2} radians, we multiply by 180π\frac{180}{\pi} to convert to degrees.\newlineθ\theta in degrees = (π2)×(180π)\left(\frac{\pi}{2}\right) \times \left(\frac{180}{\pi}\right)
  3. Simplify expression: Simplify the expression by canceling out the π\pi in the numerator and the denominator.θ\theta in degrees = (π2)×(180π)=1802=90\left(\frac{\pi}{2}\right) \times \left(\frac{180}{\pi}\right) = \frac{180}{2} = 90
  4. Check answer choices: Check the answer choices to find the one that matches the calculated value of θ\theta in degrees.\newlineThe correct answer is (B) 90∘90^\circ.

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