To convert an angle from degrees to radians, you can use the following relationship:
[tex]\[ \text{Radians} = \text{Degrees} \times \left( \frac{\pi}{180} \right) \][/tex]
Given an angle of 210°, we can follow these steps:
1. Identify the given angle in degrees:
The given angle is 210°.
2. Convert degrees to radians:
To convert degrees to radians, multiply the degree measure by [tex]\(\frac{\pi}{180}\)[/tex]:
[tex]\[
210^\circ \times \left( \frac{\pi}{180} \right)
\][/tex]
3. Carry out the multiplication:
Simplify the fraction and calculate the radian measure:
[tex]\[
210^\circ \times \left( \frac{\pi}{180} \right) = \frac{210\pi}{180} = \frac{21\pi}{18} = \frac{7\pi}{6}
\][/tex]
So, the angle in radians is:
[tex]\[
\frac{7\pi}{6} \approx 3.6651914291880923
\][/tex]
Next, let's draw the angle of 210° in standard position:
1. Draw the coordinate system:
Draw the x-axis (horizontal line) and y-axis (vertical line) intersecting at the origin (0,0).
2. Identify the initial side:
The initial side of the angle in standard position lies along the positive x-axis.
3. Rotate the initial side counterclockwise:
Rotate the initial side counterclockwise until it reaches 210°. Since 210° is greater than 180°, the terminal side will also be in the third quadrant (between 180° and 270°).
4. Place the terminal side:
Mark the terminal side 30° past the -x axis (since 210° - 180° = 30°). This means the terminal side of the angle lies in the third quadrant.
The final diagram will show the initial side along the positive x-axis and the terminal side extending into the third quadrant, creating an angle of 210° measured counterclockwise from the positive x-axis.
