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Convert the angle theta=(5pi)/(12) radians to degrees. Express your answer exactly. theta=◻" 。 "

Convert the angle θ=5π12 \theta=\frac{5 \pi}{12} radians to degrees.\newlineExpress your answer exactly.\newlineθ=□∘ \theta=\square^{\circ}

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Full solution

Q. Convert the angle θ=5π12 \theta=\frac{5 \pi}{12} radians to degrees.\newlineExpress your answer exactly.\newlineθ=□∘ \theta=\square^{\circ}
  1. Understanding radians and degrees: Understand the relationship between radians and degrees.\newlineOne complete revolution around a circle is 2π2\pi radians or 360360 degrees. Therefore, the conversion factor between radians and degrees is 180π\frac{180}{\pi}.
  2. Setting up the conversion formula: Set up the conversion from radians to degrees for θ\theta.θ in degrees=θ in radians×(180π)\theta \text{ in degrees} = \theta \text{ in radians} \times \left(\frac{180}{\pi}\right)
  3. Substituting the given value: Substitute the given value of θ \theta in radians into the conversion formula.θ \theta in degrees = (5π12)×(180π) \left(\frac{5\pi}{12}\right) \times \left(\frac{180}{\pi}\right)
  4. Simplifying the expression: Simplify the expression by multiplying the numerators and canceling out the π\pi terms.θ\theta in degrees = 5×18012\frac{5 \times 180}{12}
  5. Calculating the final value: Divide 5×1805 \times 180 by 1212 to find the value of θ\theta in degrees.\newlineθ\theta in degrees = 90012\frac{900}{12}
  6. Calculating the final value: Divide 5×1805 \times 180 by 1212 to find the value of θ\theta in degrees.\newlineθ\theta in degrees = 90012\frac{900}{12} Calculate the final value.\newlineθ\theta in degrees = 7575

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