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Convert the angle θ=17π18\theta=\frac{17\pi}{18} radians to degrees.\newlineExpress your answer exactly.\newlineθ=□∘\theta=\square^{\circ}

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Full solution

Q. Convert the angle θ=17π18\theta=\frac{17\pi}{18} radians to degrees.\newlineExpress your answer exactly.\newlineθ=□∘\theta=\square^{\circ}
  1. Convert to degrees: To convert radians to degrees, we use the conversion factor 180180 degrees =π= \pi radians.\newlineSo, we multiply θ\theta by 180π\frac{180}{\pi}.\newlineCalculation: θ=17π18×180π\theta = \frac{17 \pi}{18} \times \frac{180}{\pi}.
  2. Simplify expression: Simplify the expression by canceling out π\pi from the numerator and denominator.\newlineCalculation: θ=1718×180\theta = \frac{17}{18} \times 180.
  3. Multiply and divide: Now, multiply 1717 by 180180 and then divide by 1818. Calculation: θ=(17×180)/18\theta = (17 \times 180) / 18.
  4. Perform final division: Perform the multiplication and division.\newlineCalculation: θ=306018\theta = \frac{3060}{18}.
  5. Obtain exact value: Finally, divide 30603060 by 1818 to get the exact value in degrees.\newlineCalculation: θ=170\theta = 170 degrees.

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