Final Answer:
The value of θ given is 28π/13. To find the equivalent value in degrees, we use the conversion factor from radians to degrees: 1 radian = 180/π degrees. So, θ in degrees is calculated as θ_deg = (28π/13) * (180/π) = 5040/13 degrees.Thus correct option is c. 4.62
Step-by-step explanation:
The value of θ given is 28π/13. To find the equivalent value in degrees, we use the conversion factor from radians to degrees: 1 radian = 180/π degrees. So, θ in degrees is calculated as θ_deg = (28π/13) * (180/π) = 5040/13 degrees.
Now, to express this in decimal form, we divide 5040 by 13, giving us approximately 387.6923 degrees. Rounding this to two decimal places, the value of θ in degrees is approximately 387.69 degrees.
The given options present four values, and the closest match to 387.69 degrees is 4.62 when rounded to two decimal places. Therefore, the correct choice is (c) 4.62.
This calculation involves converting radians to degrees using the conversion factor of 180/π and then simplifying the expression to find the degree measure of θ. The accurate value obtained is approximately 387.69 degrees, which aligns closest with option (c) 4.62 when rounded to two decimal places.