Convert 11 pi over 6 radians into degrees.
Understand the Problem
The question is asking to convert the angle measurement of 11π/6 radians into degrees. This involves using the conversion factor that 180 degrees equals π radians.
Answer
$330$ degrees
Answer for screen readers
$330$ degrees
Steps to Solve
- Identify the conversion factor
To convert radians to degrees, we use the conversion factor that $180$ degrees is equal to $\pi$ radians.
- Set up the conversion
To convert $11\pi/6$ radians to degrees, we multiply it by the conversion factor: $$ 11\pi/6 \times \frac{180}{\pi} $$
- Simplify the expression
When multiplying, the $\pi$ in the numerator and denominator cancels out: $$ 11 \times \frac{180}{6} $$
- Calculate the degree measurement
Now, simplify $180/6$, which equals $30$: $$ 11 \times 30 = 330 $$
- Final result
Thus, $11\pi/6$ radians is equal to $330$ degrees.
$330$ degrees
More Information
The angle $330$ degrees is in the fourth quadrant of the unit circle. It is an equivalent angle for $-30$ degrees. This conversion is important for understanding the relationships between angles in different measurements.
Tips
- Forgetting to simplify after multiplying the radians value by the conversion factor.
- Confusing the order of the multiplication which can lead to wrong results.
