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If theta=(4pi)/(9) radians, what is the value of theta in degrees? Choose 1 answer: (A) 20^(@) (B) 36^(@) (c) 80^(@) (D) 720^(@)

If θ=4π9 \theta=\frac{4 \pi}{9} radians, what is the value of θ \theta in degrees?\newlineChoose 11 answer:\newline(A) 20∘ 20^{\circ} \newline(B) 36∘ 36^{\circ} \newline(C) 80∘ 80^{\circ} \newline(D) 720∘ 720^{\circ}

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Inverses of sin, cos, and tan: degreesright chevron icon

Full solution

Q. If θ=4π9 \theta=\frac{4 \pi}{9} radians, what is the value of θ \theta in degrees?\newlineChoose 11 answer:\newline(A) 20∘ 20^{\circ} \newline(B) 36∘ 36^{\circ} \newline(C) 80∘ 80^{\circ} \newline(D) 720∘ 720^{\circ}
  1. Conversion factor for radians to degrees: To convert radians to degrees, we use the conversion factor that π\pi radians is equal to 180180 degrees. Therefore, we multiply the given radian measure by 180π\frac{180}{\pi} to convert it to degrees.\newlineCalculation: θ\theta in degrees = θ\theta in radians ×(180π)\times \left(\frac{180}{\pi}\right)\newlineθ\theta in degrees = (4π9)×(180π)\left(\frac{4\pi}{9}\right) \times \left(\frac{180}{\pi}\right)
  2. Calculation of θ\theta in degrees: Now, we simplify the expression by canceling out the π\pi in the numerator and the denominator.\newlineCalculation: θ\theta in degrees = (49)×180\left(\frac{4}{9}\right) \times 180
  3. Simplification of the expression: Next, we multiply 44 by 180180 and then divide by 99 to find the value of θ\theta in degrees.\newlineCalculation: θ\theta in degrees = (4×180)/9(4 \times 180) / 9\newlineθ\theta in degrees = 720/9720 / 9
  4. Calculation of θ\theta in degrees: Finally, we perform the division to get the value of θ\theta.\newlineCalculation: θ\theta in degrees = 7209\frac{720}{9}\newlineθ\theta in degrees = 8080

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