Convert the angle θ from radians into degrees, minutes, seconds. Round to the nearest second.
θ=16π/17
check my work please and thank you
16pi/17=169.41176=169 degrees
.41176 x 60= 24.708 minutes = 25 minutes
.708 x 60=42.48=42 seconds
169 degrres, 25 minutes, 42 seconds
correct? thanks again
rounding is for the seconds
the minutes should not be rounded
16pi/17 x 180/pi= 169.41176 (thatś how I got the first part)
To convert an angle from radians to degrees, minutes, and seconds, you can follow these steps:
1. Convert the angle from radians to degrees: To do this, you need to multiply the angle in radians by the conversion factor of 180/π. So, θ in degrees = (16π/17) * (180/π) = 169.41176 degrees (rounded to six decimal places).
2. Now, we need to break down the decimal part of the degrees into minutes and seconds. To convert fractional degrees to minutes, you multiply the decimal part by 60. In this case, 0.41176 * 60 = 24.7056 minutes (rounded to four decimal places), which can be rounded up to 25 minutes.
3. Then, we need to convert the fractional minutes to seconds. Multiply the decimal part of the minutes by 60. So, 0.7056 * 60 = 42.336 seconds (rounded to three decimal places), which can be rounded up to 42 seconds.
Therefore, the angle θ = 16π/17 radians is approximately equal to 169 degrees, 25 minutes, 42 seconds. Your conversion is correct.