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Convert the angle theta=(9pi)/(5) radians to degrees. Express your answer exactly. theta=◻" 。 "

Convert the angle θ=9π5 \theta=\frac{9 \pi}{5} radians to degrees.\newlineExpress your answer exactly.\newlineθ=□∘ \theta=\square^{\circ}

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Full solution

Q. Convert the angle θ=9π5 \theta=\frac{9 \pi}{5} radians to degrees.\newlineExpress your answer exactly.\newlineθ=□∘ \theta=\square^{\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.
  2. Multiplying the given angle in radians: We multiply the given angle in radians by the conversion factor (180/π)(180/\pi) to get the angle in degrees.\newlineθ=(9π/5)×(180/π)\theta = (9\pi/5) \times (180/\pi)
  3. Simplifying the expression: Simplify the expression by canceling out the π\pi terms.θ=(95)×180\theta = \left(\frac{9}{5}\right) \times 180
  4. Performing the multiplication: Perform the multiplication to find the value of θ\theta in degrees.\newlineθ=9×36\theta = 9 \times 36
  5. Calculating the final answer: Calculate the product to get the final answer. θ=324\theta = 324 degrees

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