Question

Sophia is trying to open a door by turning the doorknob.

Door Knob Free Stock Photo - Public Domain Pictures

Activity 1 of 2
A certain doorknob must turn 40 degrees in order to open a door. What is this angle measurement as a radian measure?

Answer 1

To convert degrees to radians, you can use the conversion factor \(\frac{\pi \text{ radians}}{180 \text{ degrees}}\).

To convert 40 degrees to radians, use the following formula:

\[
\text{radians} = \text{degrees} \times \frac{\pi \text{ radians}}{180 \text{ degrees}}
\]

Substituting in the value:

\[
\text{radians} = 40 \times \frac{\pi}{180}
\]

Now simplify the fraction:

\[
\text{radians} = 40 \times \frac{\pi}{180} = \frac{40\pi}{180} = \frac{2\pi}{9}
\]

Thus, 40 degrees is equivalent to \(\frac{2\pi}{9}\) radians.